I have done questions 2,4,6, and 8.
2.) Explain why you need to find the circumference of a circle to find the surface area of a cylinder?
This is what I think.
You need to find the circumference of a circle to find the surface area of a cylinder because in order to find the surface area, in the end you have to add it up to get your TOTAL SURFACE AREA.
4.) Estimate the surface area of each cylinder. Then, calculate each surface area to the nearest cenimetre.
This is what I did.
On the first cylinder it is d = 7cm and the height is 30cm.
*remember to write down your formula because you can lose a half mark on a test!*
(pi x r 2) + (pi x d x h) = Total surface area
A.) d/2 = r
7/2 = 3.5cm2
(3.14 x 3.5 x 3.5)+(3.14 x 7 x 30) = 697.86cm2
38.46cm2 + 659.4cm2 = 697.86cm2
Total Surface Area = 697.86cm2
(pi x r 2)+(pi x d x h) = Total surface area
B.)(3.14 x 10 x 10)+(3.14 x 20 x 22) = 1695.6cm2
314cm2 + 1381.6cm2 = 1695.6cm2
Total Surface Area = 1695.6cm2
6.) Use the formula, (pi x r 2)+(pi x d x h) to calculate the surface area of each object. Give your answer to the nearest hundredth of a square unit.
A.)(3.14 x 1.25 x 1.25)+(3.14 x 2.5 x 10)
4.90cm2 + 78.5cm2
Total Surface Area = 83.4cm2
B.) d/2= r
(3.14 x 2.5 x 2.5)+(3.14 x 5 x 7)
19.62cm2 + 109.9cm2
Total Surface Area = 129.52cm2
8.) Anu wants to re-cover the cylindrical stool in his bedroom. how much material will he need if there is no overlap and he does not cover the bottom of the stool.
This is what I did.
Formula = (pi x r x r)+(pi x d x h)
42/2 = 21
(3.14 x 21 x 21)+(3.14 x 42 x 32)
1384.71cm2 + 4220.16cm2 - 21 =
Total Surface Area = 5583.87cm2
Here is a link on cylinder and a little bit about Volume!
Here is a link to a helpful video.
Cylinder Problems from 7.3
A.) Volume = (pi x r x r) x h
d/2 = r 8/2 = r r = 4 cm
(3.14 x 4 x 4) = 50.24 cm^2
50.24 cm^2 x 12 cm = 602.88 cm^3
Volume = 602.88 cm^3
B.) Volume = ( pi x r x r) x h
d/2 = r 2/2 = r r = 1 cm
(3.14 x 1 x 1) = 3.14 cm^2
3.14 cm^2 x 7 = 21.98 cm^3
Volume = 21.98 cm^3
C.) Volume = ( pi x r x r ) x h
d/2 = r 12/2 = r r = 6 cm
( 3.14 x 6 x 6 ) = 113.04 cm^2
113.04 cm^2 x 37.5 = 4239 cm^3
Volume = 4239 cm^3
D.) Volume = ( pi x r x r ) x h
d/2 = r 4.5/2 = r r = 2.25 cm
( 3.14 x 2.25 x 2.25 ) = 15.89625 cm^2
15.89625 cm^2 x 19.5 = 309.976875 cm^3
Volume = 309.976875 cm^3
Cylinder problems from 7.4
A.) Yes, he does have enough small prisms.
B.) The volume of the new prism is 22.4672^3
Here is what I did.
V= B x h / 2 x h
V = 5.6 x 6.8 / 2 = 19.04 x 1.18 = 22.4672^3