Everything Maths Grade 10

Worked example 19: Multiplying the dimensions of a rectangular prism byk

QUESTION

Prove that if the height of a rectangular prism with dimensionsl,bandhis multiplied by a constant value of
k, the volume will also increase by a factork.

h

b

l

SOLUTION

Step 1: Calculate the original volume

We are given the original dimensionsl,bandhand so the original volume isV=lbh.

Step 2: Calculate the new volume

The new dimensions arel,b, andkhand so the new volume is:

Vn=lb(kh)

=k(lbh)

=kV

Step 3: Write the final answer

If the height of a rectangular prism is multiplied by a constantk, then the volume also increases by a factor of
k.

Worked example 20: Multiplying the dimensions of a cylinder byk

QUESTION

Consider a cylinder with a radius ofrand a height ofh. Calculate the new volume and surface area (expressed
in terms ofrandh) if the radius is multiplied by a constant factor ofk.

r

h

454 13.4. The effect of multiplying a dimension by a factor ofk