Respuesta :

[tex]\huge{ \mathcal{  \underline{ Answer} \:  \:  ✓ }}[/tex]

The given values are :

  • height (h) = 8 in

  • radius (r) = 5 in

We know,

[tex] \large\boxed{ \mathrm{slant \: \: height} = \sqrt{h {}^{2} + r {}^{2} } }[/tex]

  • [tex]l = \sqrt{ {h}^{2} + r {}^{2} } [/tex]

  • [tex]l = \sqrt{8 {}^{2} + {5}^{2} } [/tex]

  • [tex]l = \sqrt{64 + 25} [/tex]

  • [tex]l = \sqrt{89}[/tex]

Now,

[tex] \large \boxed{\mathrm{lateral \: \: surface \: \:a rea } = \mathrm{\pi rl}}[/tex]

  • [tex]\pi \times 5 \times \sqrt{89} [/tex]

  • [tex] \mathrm{5\pi \sqrt{89 } \: \: in {}^{2} }[/tex]

Therefore the correct answer is :

D. 5π√89 in²

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[tex]\mathrm{ ☠ \: TeeNForeveR \:☠ }[/tex]

abidemiokin

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

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