1. The corner of a square room needs to be covered in carpet. A triangular piece is needed. If one side has to be 5 feet and the other needs to be 7 feet, what area needs to be covered?
2. You are making a flag with two colours. The flag is sewn so the cloth meets a the middle of the flag going diagonally downwards. If you can get exactly the cloth cut exactly as you need it, how much cloth of each colour, in square feet, is needed if the flag’s dimensions are 4 feet by 3 feet.
3. A diamond window is made from four panes of glass, which meet at a “t” in the middle. The T is 1 meter high and 50 centimetres wide. If the bottom left pane of glass breaks, how much glass is needed to replace it?
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area is base * height didided by 2
ReplyDeletesince room is square then the corner is a right angled triangle.
so area = 5 * 7 /2
= 35/2
area = 17.5 squared feet
how much questions do we hav to do
ReplyDeletesolution 2
ReplyDeletefirst we find the area of the rectangle
Area = base * height
area = 3 * 4
area = 12 sqa ft
cutting this rectangle in half gives two 2 triangles.
we can then find the area of the triangles
a = 1/2(b) * h
a = 1/2(3) * 4
a = 1.5 * 4
a = 6
ANSWER: 6 sq.ft of 1 colours & 6 sq.ft of another colour
what is a sinewave?
ReplyDeletesince the t is at the middle of the diamond .you can divide d diamond into 4 right angle triangles
ReplyDeletearea = height * base /2
area = 50 *25 /2
area =1250 /2
= 625 square cm
if you wanted to know the area of the diamond
ReplyDeleteuse the formula
area = 1/2 (product of diagonals)
so the area of the diamond above would be
area = 1/2 (100 * 50)
area = 1/2 (5000)
area = 2500 sq cm
cre go to this website for description and diagrams of trig curves:
ReplyDeletewww.intmath.com/Trigonometric-graphs/1_Graphs-sine-cosine-amplitude.php - 25k
but we didnt want the area of the entire diamond
ReplyDeleteQ1
ReplyDeleteshotta was rite in reconizin dat d room was sq and there4 d corner was a right angle triangle.
Given dis info we can therefore use d formula which is base from high all over 2.
so hence:
area = ( 5*7 )/ 2
= 35/2
=17.5 sq feet
Q3
ReplyDeleteGiven the figure is a diamond and h=100cm and w= 50cm,
assuming the t cuts exactly at the middle h= 100/2=50cm, w= 50/2= 25 cm,
there are now 4 triangles within the diamond therefore the area of 1 triangle will be
A=(50 *25)/2=625 sq cm
A sailboat has a triangular sail, mounted on an L-Shaped frame which is 15 feet tall and ten feet long. A bird flies into the sail and rips it. How much canvas is needed to replace the sail?
ReplyDeleteA wedge shaped tank is built along the length of a straight wall that measures 60 feet, and goes halfway up the wall, which is 40 feet high. If the base of the tank extends 10 feet from the perpendicular point where the wall meets the ground. How much is the capacity of the tank?
A box is a cube, with one side being 50 centimetres. What is the volume of the box?
An ice cube maker makes perfect ice cubes, 5 centimetres tall. What volume of water is needed to make each ice cube?
An automatic lawn mower is programmed to mow a square playing field with a 100 metre length. How many square feet must the lawn mower be programmed to cut?
The painting company owns billboards, and one of their clients has not paid the bill for this month. The company needs to cover the billboard with a blank screen to cover the ad. The billboard’s screen stands 20 feet high and 40 feet across, how much screen material is needed to cover it?
A house is built with a flat concrete roof, which is to be covered completely in vinyl tiles. If each tile is a square, measuring 1 foot across one side, how many tiles are needed if the roof is 100 feet across and 75 feet wide?
area = base * height / 2
ReplyDeletearea = 10 x 15 / 2
area = 150/2
area = 75 sq feet
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ReplyDeleteq3
ReplyDeleteVolume of Cube = s x s x s
therefore, Vol of cube = 50 x 50 x 50
vol of cube = 125000 cm cubed
q4
ReplyDeleteVolume = sxsxs
volume of cube = 5x5x5
volume of cube = 125 cm cubed
q5
ReplyDeletearea of square = s x s
area of square = 100 x 100
area of square = 10000 squared meters
assuming the wedge is rectangular, the area of the tank would be (L*B*H)
ReplyDeleteSO = 60*10*20
=12000 cubic feet
Please post another question after you've answered so someone else can.
ReplyDelete11. A cricket pitch is 20 metres long, and 6 metres wide. There is a test match about to be played, and the organizers need to know what size of cover to bring for the pitch in case of rain. What size of cover do they need?
ReplyDelete12. A swimming pool measures 100 metres long, and contains eight lanes, with each lane being 6 metres wide. If the pool is 3 metres deep, how much water does the pool contain?
13. The owners of the pool in question 11 decide it’s a good idea to get a cover for the pool when it’s not in use. The cover needs to overlap one metre on each side of the pool to be secured. How much material is needed to cover the pool?
14. Your mother is designing a new room in the house that is a perfect circle, and needs to purchase carpet for the floor. The distance across the centre of the room, from one side to the next, is 20 metres. Exactly how much carpet will be needed to cover the floor?
15. You finish eating a can of Pringles, and now want to know if putting water in the can will make the water taste like Pringles. If the Pringles can is 30 centimetres high, and has a diameter of four centimetres, how much water will fill the can?
solution 1
ReplyDeletesince the pitch is a rectangle
The area of a rectangle can be found by multiplying the base times the height.
area = L *B
area = 20 * 6
area = 120
answer = 120M
solution 2
ReplyDeletefor this question we find the surface area of the pool then multiple it by the height of the pool.
so
volume = L*B*h
volume = 100*48*3
volume = 14400
answer = 14400 cubic Meters
solution 3
ReplyDeletefor this question we find the surface area of the pool but increases the lenght and breath
new lenght = 102m
new breath = 50m
area = L*B
area = 102 * 50
area = 5100 sq M
solution 4
ReplyDeletefor this question we are findin the area of a circle which is:
area = pie * radius(sq)
from question
pie = 3.14
radius = 10
so
area = 3.14 * 10 *10
area = 314
answer = 314 sq. M
solution 5
ReplyDeletefor this question we must find the surface area of any side of the pringle can then multiple it by the height of the pringle can
so
surface area of pringle can is
area of circle = pie * radius * radius
area of circle = 3.14 * 2 * 2
area of circle = 12.56
therefore
volume = 12.56 * 30
volume = 376.8
answer = 376.8 cm cube
16. Caculate the area of a triangle having sides of lengths 12cm, 15cm and 18cm.
ReplyDeleteWhat is the perpendicular height of the vertex opposite the side of the length 15cm
17. A swimming pool measures 200 metres long, and contains eight lanes, with each lane being 16 metres wide. If the pool is 13 metres deep, how much water does the pool contain?
18. The owners of the pool in question 17 decide it’s a good idea to get a cover for the pool when it’s not in use. The cover needs to overlap 5 metres on each side of the pool to be secured. How much material is needed to cover the pool?
19. A cylinder is cast from a rectangular piece of alloy of dimensions 5cm by 7cm by 12cm. The length of the cylinder must be 60cm. Determine the diameter of the cylinder.
20. A field measures 60m by 25m. A grow box 2m wide is made along the two short sides and one long side. A hut 3m square together with a circular pool is built at one end of the field. What is the area remaining?
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ReplyDelete17)
ReplyDeletel- 200m
w=(16*8)=128
d=13
volume= 200*128*13
=332800 m^3
18)
ReplyDeletewell in real life u will want a cover that look like a rectangle but the question ask for 5 m on EACH side so;
if u have the area of the surface of the pool which is 200*128=25600 m^2 and the owners want 5 m more on each side then u just need 2 add
{2 *(5m *200m)} +{2 (5 m * 128m)} to the area which is 25600 m^2 so it will be 288,80 m^2
but if u add 10 m to l and w so; (128+10m) *(200+10) = 28980 m^2
as u see u don’t get the same answer thats because the answer with 288,80 m^2 does not accommodate the 4 corners (5m*5m) but the question asked for each side (4 sides) to have 5m more so the answer is 288,80 m^2 but in real life the owners will not want a cover with 4 corners missing so the area of the cover will be 28980 m^2 in real life.
19)
ReplyDeleteVol of rectangular piece of alloy = 5*7*12= 440 cm^3
Vol of cylinder = (πr^2)*60=440 cm^3
440/60= πr^2
7.3333=πr^2
7.333/π=r^2
2.3342=r^2
r=1.52
diameter =2r =3.04cm
20
ReplyDeleteField= 60 *25 =1500 m^2
3 grow box ={2*(2*25)}+(2*56) =212 m^2
Hut=3*3=9 m^2
U didn’t give the r of pool but if u mean that the hut side is the diameter of the pool the r =1.5m.
Pool =π (1.5 )^2 =7.06 m^2
So 7.06+9+212= 228.06 m^2
1500-228.06 = 1271.94 m^2 that remains
Solution for Q1.
ReplyDeletearea is: half base * height, over two.
beacuse the room is square, the corner is a right angled triangle.
therefore: area = 5 * 7 /2
= 35/2
area = 17.5 squared feet
solution for Q2.
ReplyDeleteIn this case it is two right angle triangles .
so we then find the area of the rectangle
Area = base * height
area = 3 * 4
area = 12 sqa ft.
divide this rectangle into two right angle equal triangles.
we can then find the area of the triangles
a = (b * h)/2
a = (3 * 4)/2
a = 6
ANS: 6 sq.ft of 1 the first colour,and 6 sq.ft of another colour.
solution for Q3.
ReplyDeleteGiven that, the figure is a diamond and h=100cm
w= 50cm,
and that t cuts exactly at the middle
h= 100/2 =50cm
w= 50/2= 25 cm
there are 4 triangles in the diamond, therefore the area of 1 triangle will be
Area =(50 *25)/2
=625 sq cm.
(q10)since no one attempted question ten
ReplyDeletearea of the concrete roof is = L*B
=100*75
= 7500 suared feet
since we want the number of tiles that will cover the roof
no of tiles = area of roof/area of one tile.
no of tiles = 7500foot^2/1foot^2
= 7500 tiles
Problem 2
ReplyDeleteArea=base*height
area=3*4
therefore answer is 12 square ft
Area of rest of triangles
area=base*height/2
=3*4/2
=6
Problem 19
ReplyDeleteVolume-rectangulart piece of alloy=5*7*12
=440^3
Volume of cylinder=Pie*radius squared*60=440cm^3
440/60=pie*radius squared
7.33=pie radius squared.
radius=1.52
therefore diameter= 3.04
problem 3
ReplyDeleteLength=102m
Breath=50
Area=length*breath
Area=102*50
area = 5100sq miles
length=200meters
ReplyDeletewidth=16*8
=128
D=13
volume=200*128*13
=332800m^3
Problem 4)
ReplyDeleteArea of circle=pie*radius squared
Radius=10
Area=3.14*10*10
=314square meters.
wat problems u doin star?
ReplyDeleteThe following is a question i came across. It may not be that difficult but i am still looking for more that are a little more challenging.
ReplyDeleteA designer works on a design for a paper cup which folds flat. His design uses the shape of an upturned pyramid with a squared base. The dimensions of the cup are:
lenght of side of opening= 6cm
depth=10cm
What is the cup's volume?
SOLUTION TO MY QUESTION
ReplyDeleteok so the info that is given are
it is a pyramid with square base
length of side of opening= 6cm
depth=10cm
the length of the opening is the length of the side of the square base.
the depth of the pyramid is the height.
volume of pyramid= 1/3 Ah
where A is the area of the base an h is the height
A=s*s (area of square)
=6*6
=36cm sq
vol=1/3*36*10
=120cm cube
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ReplyDeletewhat is meant by the "paper cup which folds flat"..not 3D and its a pyramid
ReplyDeletearea of triangle=base*height/2
ReplyDeletetherefore area =5*7/2
=35/2
answer=17.5 square feet
what question impersonator
ReplyDeletei see your question now the dawg its enclosed with a flat base and four triangles...whey
ReplyDeletea concrete dome is in the shape of a hemisphere. its internal and external diameters are 4.8 meters and 5 meters respestively. calculate the volume of concrete used to cast the dome?
ReplyDeletesolution
ReplyDeletethe volume of a sphere is (4/3*pie*radius cubed)/2
therefore V of the large hemisphereis
= (4/3*pie*2.5^3)/2
= 65.4/2
= 32.7 meters cubed
the area of the inner hemisphere is
= (4/3*pie*2.4^3)2
= 57.9/2
= 28.95 meters cubed
volume of concrete used = outer hemisphere-inner hemisphere.
= 32.7-28.95
volume of concrete used = 3.75 cubic meters
an inverted cone has a diameter of 2.1m and height of 2.1m. if the cone is to be lined with lead,calculate the surface area of lead required.
ReplyDeletesolution.
ReplyDeletesurface area of a cone = pie*radius*L
where L is slant length.
if we know the radius and we know the perpendicular height then
by phy.therom L^2 = 1.05^2+2.1^2
L = 2.58
area of cone = pie * 1.05 * 2.58
= 8.5 sqared meters
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ReplyDeletecorrection to shotta question
ReplyDeletearea of cone =22/7*r*l
l is found by phy. therom=1.05^2+2.1^2= 2.35
area of cone =22/7*1.05*2.35
=7.76 sqared meters
Find the surface area (to the nearest cm sq) of a sphere with:
ReplyDeleteA)radius=12.6cm
B)diameter=784mm
SOLUTION
ReplyDeleteA)r=12.6cm
A=4pie*r^2
= 4*pie*12.6^2
=1995.036999
therefore area= 1995cm sq (to nearest cm)
SOLUTION
ReplyDeleteB)diameter=784mm
in cm=784/10=78.4cm
radius=78.4/2=39.2
therefore A=4*pie*39^2
=19309.99874
therefore surface A=19310cm sq (nearest cm)
4)
ReplyDeletetriangular sail has:1)15 ft as height
2)10 ft as lenght
to calculate the area of a tiangle [h*b/2]is used
therefor,
area=15*10/2=75
the area of triangular sail=75 squared ft
there are 8 lanes of the pool
ReplyDeleteand every lane it 16m wide
therefore,the total width =16*8
= 128m
the volume of the pool=128*13*200
=332800 m^3
the new room has a diameter of 20m
ReplyDeleteto carpet the room the surface area of the room must me calculated:
area of circle = pie*the square radius of the circle .
therefor,
area=3.14*400
=1256 squared m
19
ReplyDeletesince cylinder is cast from a rectangular piece of alloy the volume of rectanglar piece will equal to the cylinders volume
therefor,
the volume of the rectangular piece of alloy = 5*7*12= 440 cubic cm
volume of cylinder = (pie*the square radius of the circle)*60=440 cm^3
πr^2=7.3
r^2=7.3/π
r=1.5
diameter =2r =3cm
volume of box = s x s x s
ReplyDeletetherefore,
volume of cube = 50 x 50 x 50
volume of cube = 125000 cm cubed
Find the curved surface area of a cone,correct to 1 decimal place with:
ReplyDeleteA)radius=48cm
slant height=25cm
B)slant height=35cm
diameter=15cm
SOLUTION A
ReplyDeleteinfo given
radius=48cm
slant height=25cm
curved surface area of a cone=pie*r*l
r=48cm
l=25cm
C=pie*48*25
=3769.911184
therefore curved surface area= 3769.9 cm sq (1dp)
SOLUTION B
ReplyDeleteinfo given
slant height=35cm
diameter=15cm
r=15/2=7.5cm
l=35cm
curved surface area of a cone=pie*r*l
=pie*7.5*35(1dp)
=824.668 0761cm
=824.7 cm sq
first we find the area of the rectangle
ReplyDeleteArea = base * height
area = 3 * 4
area = 12 sqa ft
cutting this rectangle in half gives two 2 triangles.
we can then find the area of the triangles
a = 1/2(b) * h
a = 1/2(3) * 4
a = 1.5 * 4
a = 6
Question??
ReplyDeleteA concrete truck arrives at a job site holding 7.8 cubic yards of concrete. If the patio being constructed is 18 feet across and 4 inches thick, how long will the patio be if constructed from the amount of concrete on the truck?
A die is a cube molded from hard plastic. The edge of a typical die measures 0.62inches. Dice are usually produced in a mold which holds 100 die at one time. To the nearest cubic inch, how much plastic is needed to fill this large mold?
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ReplyDelete