Question

Two cylinders, A and B, are mathematically similar. The height of B is twice the corresponding height of A.
 The volume of A is 13 cm^3. Find the volume of B.

Answer 1

The volume of B is 39cm³

Explanation:

Volume of cylinder A

Va = 1/3πr²ha ...(1)

Where height of A is ha

If the height of B is twice the corresponding height of A

hb = 3ha

Volume of B Vb = 1/3πr²(3ha)...(2)

If volume of A is 13cm³ and

Va = 1/3πr²ha

Then 13 = 1/3πr²ha

39 = πr²ha

πr² = 39/ha ... (3)

To get Vb, we wil substitute equation 3 into 2 to have;

Vb = 1/3(39/ha)(3ha)

Vb = 39/ha × ha

Vb = 39cm³

Answer 2

104 cm^3

Explanation:

The ratio of volumes is the cube of the ratio of linear dimensions for similar figures. Since the height of B is 2 times the height of A, the volume of B will be 2^3 = 8 times the volume of A, so is ...

8·13 cm^3 = 104 cm^3