Question

The volume of a certain right circular cylinder is 16. A larger circular cylinder has radius 25% greater and height 50% greater than the radius and height respectively, of the smaller cylinder. What is the volume of the larger cylinder

Answer 1

Answer:

$V_2 = 37.5$

Step-by-step explanation:

Given

$Volume = 16$

Represent the height of the smaller cylinder with h and its radius with r.

The height (H) of the larger cylinder is

$H = h + 50\% * h$

And the radius (R) is;

$R = r + 25\% * r$

Required

Determine the volume of the larger cylinder

Volume of the smaller cylinder is:

$V_1 = \pi r^2h$

Substitute 16 for V1

$16 = \pi r^2h$

While the volume of the larger cylinder is:

$V_2 = \pi R^2H$

We have that:

$H = h + 50\% * h$ and $R = r + 25\% * r$

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Simplify both expressions

$H = h + 50\% * h$

$H = h + 0.50*h$

$H = h + 0.50h$

$H = 1.50h$

$R = r + 25\% * r$

$R = r + 0.25*r$

$R = r + 0.25r$

$R = 1.25r$

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Substitute values for R and H in $V_2 = \pi R^2H$

$V_2 = \pi * (1.25r)^2 * 1.50h$

$V_2 = \pi * 1.5625r^2 * 1.50h$

Collect Like Terms

$V_2 = 1.50 * 1.5625* \pi*r^2 * h$

$V_2 = 2.34375* \pi*r^2 * h$

$V_2 = 2.34375* \pi r^2h$

Recall that: $16 = \pi r^2h$

$V_2 = 2.34375* 16$

$V_2 = 37.5$

Hence, the volume of the larger cylinder is 37.5