Question

Calculate the volume of the following shapes. Use the approximation of pi.

1) A sphere with a radius of 4.5 cm
2) A cylinder with a radius of 2.1 cm and a height of 8.0 cm
3) A cone with a radius of 8.0 cm and a height of 2.0 cm

Please explain your work!

Answer 1

Note: I'm assuming that your teacher wants you to use the approximation pi = 3.14
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Problem 1)

Plug the value r = 4.5 into the formula below to find the approximate volume

V = (4/3)*pi*r^3
V = (4/3)*pi*(4.5)^3
V = (4/3)*pi*91.125
V = (4/3)*91.125*pi
V = 121.5*pi
V = 121.5*(3.14)
V = 381.51

So the approximate volume of this sphere is roughly 381.51 cubic cm

Note: we can write "cubic cm" as "cm^3"
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Problem 2)

The formula to use for the volume of a cylinder is
V = pi*r^2*h
where r is the radius and h is the height

In this case, we have r = 2.1 and h = 8.0

V = pi*r^2*h
V = pi*(2.1)^2*8.0
V = pi*4.41*8.0
V = pi*35.28
V = 35.28*pi
V = 35.28*(3.14)
V = 110.7792

The volume is roughly 110.7792 cubic cm
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Problem 3)

Now we use the formula
V = (1/3)*pi*r^2*h
which is the volume of a cone. Note how this is simply 1/3 the volume of the cylinder (with same radius and height)

Use r = 8.0 and h = 2.0

V = (1/3)*pi*r^2*h
V = (1/3)*pi*(8.0)^2*(2.0)
V = (1/3)*pi*64*2
V = (1/3)*pi*128
V = (1/3)*128*pi
V = (128/3)*pi
V = (128/3)*(3.14)
V = 133.973333

The approximate volume is 133.973333 cubic cm