Chapter 12, Problem 6RP

To determine

To calculate: The volume of the cylinder if its slant height is 17 cm and height is 15 cm.

Answer to Problem 6RP

The volume of cylinder is $240\pi$ .

Explanation of Solution

Given information:

Height h = 15 cm,

Slant height l =17 cm.

Formula used:

The below theorem is used:

Pythagoras theorem states that “In a right angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides”.

  

In right angle triangle,

  $a^2+b^2\text{= }{c}^2$

Volume of cylinder $=B\times h$

B = Base area of cylinder and h = height of cylinder

Area of a circle: $A=\pi r^2$

r = radius of circle

Calculation:

  

Volume of cylinder $=B\times h$

Side BC can be calculated by applying Pythagoras Theorem.

In right angled triangle ABC , we get

  $\begin{array}{l}{\left(AC\right)}^2={\left(AB\right)}^2+{\left(BC\right)}^2\\ {\left(17\right)}^2={\left(15\right)}^2+{\left(BC\right)}^2\\ 289=225+{\left(BC\right)}^2\\ {\left(BC\right)}^2=289-225\\ {\left(BC\right)}^2=64\\ BC=\sqrt{64}=8\end{array}$

d = BC = 8

  $r=\frac{d}{2}=\frac{8}{2}=4$

Base area of cylinder:

  $\begin{array}{l}B=\pi r^2\\ B=\pi {\left(4\right)}^2\\ B=16\pi \end{array}$

The volume of cylinder:

  $\begin{array}{l}{V}_{Cylinder}=B\times h\\ V_{Cylinder}=16\pi \times 15\\ V_{Cylinder}=240\pi \end{array}$