Structure question 7 pdf

A prism that has circles as bases is called a cylinder. Recall that the formula for any prism is V = Ab

h. Since

the area of the circular base is A = πr2 , we can replace πr2 for Ab in the formula, giving us V = πr2h, where r is the

radius of the circular base, and h is the height of the cylinder.

A sphere is a three-dimensional object that has no sides. A basketball is a good example of a sphere. The vol￾ume of a sphere is given by the formula V =

4

3

πr3.

Example

Determine the volume of a sphere whose radius is 1.5'.

Replace 1.5' in for r in the formula V =

4

3

πr3.

V =

4

3

πr3

V =

4

3

π(1.5)3

V =

4

3

(3.375)π

V = 4.5π ≈ 14.14

The answer is approximately 14.14 cubic feet.

Example

An aluminum can is 6" tall and has a base with a radius of 2". Determine the volume the can holds.

Aluminum cans are cylindrical in shape, so replace 2" for r and 6" for h in the formula V = πr2h.

V = πr2h

V = π(2)2(6)

V = 24π ≈ 75.40 cubic feet

Cylinder

V = πr2h

r

h

–THEA MATH REVIEW–

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