Question

A right circular cone is a radius 5 inches and height 8 inch

Answer 1

$\huge{ \mathcal{  \underline{ Answer} \:  \:  ✓ }}$

The given values are :

• height (h) = 8 in

• radius (r) = 5 in

We know,

$\large\boxed{ \mathrm{slant \: \: height} = \sqrt{h {}^{2} + r {}^{2} } }$

• $l = \sqrt{ {h}^{2} + r {}^{2} }$

• $l = \sqrt{8 {}^{2} + {5}^{2} }$

• $l = \sqrt{64 + 25}$

• $l = \sqrt{89}$

Now,

$\large \boxed{\mathrm{lateral \: \: surface \: \:a rea } = \mathrm{\pi rl}}$

• $\pi \times 5 \times \sqrt{89}$

• $\mathrm{5\pi \sqrt{89 } \: \: in {}^{2} }$

Therefore the correct answer is :

D. 5π√89 in²

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Answer 2

The lateral surface area of the cone with a radius 5 inches and height 8 inch is 5(√89)π square inches

How to calculate the lateral area of the cone?

The formula for calculating the lateral area of the cone is expressed as:

V = 1/3πr²h

where:

• r is the radius
• h is the height

Given the following

r = 5in

h = 8n

Substitute

L = πrl
L = 5π(√8^2+5^2)
L = 5π(√89)

Hence the lateral surface area of the cone with a radius 5 inches and height 8 inch is 5(√89)π square inches

Learn more on lateral area here: https://brainly.com/question/1601740