Question

A cone has slant height of 25 inches and a radius of 7 inches as shown . What is height in inches of the cone​

Answer 1

Step-by-step explanation:

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Answer 2

The height of the cone in inches is 24 inches.

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Let's understand a few concepts:

To calculate the height of the cone we will use the following formula:

$\boxed{\bold{Slant \:height\:(l) = \sqrt{r^2 + h^2} }}$

where r = base radius of the cone and h = height of the cone

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Let's solve the given problem:

The slant height of the cone (l) = 25 inches

The radius of the cone (r) = 7 inches

Let's say "h" inches represent the height of the given cone.

Therefore, by using the above formula of slant height, we get

$l = \sqrt{r^2 + h^2}$

$\implies 25 = \sqrt{7^2 + h^2}$

• on squaring both sides

$\implies 25^2 = (\sqrt{7^2 + h^2})^2$

$\implies 25^2 = (7^2 + h^2)^\frac{1}{2} ^\times ^2$

$\implies 25^2 = 7^2 + h^2$

$\implies 625 = 49 + h^2$

$\implies h^2 = 625 - 49$

$\implies h^2 =576$

$\implies h= \sqrt{576}$

$\implies \bold{h= 24\:inches}$

Thus, the height of the given cone is 24 inches.

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