Chapter 12.5, Problem 2PSA

To determine

To calculate: The volume of a cone whose base radius is 5 and slant height is 13.

Answer to Problem 2PSA

The volume of a cone is $314.2$ .

Explanation of Solution

Given information:

Base radius of cone = 5,

Slant height of cone = 13,

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 cone $=\frac{1}{3}\times B\times h$

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

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

r = radius of circle

Calculation:

  

Side AC can be calculated by applying Pythagoras Theorem.

In right angled triangle ABC , we get

  $\begin{array}{l}{\left(AC\right)}^2={\left(AB\right)}^2+{\left(BC\right)}^2\\ {\left(13\right)}^2={\left(h\right)}^2+{\left(5\right)}^2\\ {\left(h\right)}^2=169-25\\ {\left(h\right)}^2=144\\ h=\sqrt{144}\\ h=12\end{array}$

  $B=A_{Circle}=\pi r^2=\pi {\left(5\right)}^2=25\pi$

  $\begin{array}{l}{V}_{Cone}=\frac{1}{3}\times B\times h\\ V_{Cone}=\frac{1}{3}\times 25\pi \times 12\\ V_{Cone}=100\pi \\ V_{Cone}=100\times 3.142\\ V_{Cone}=314.2\end{array}$