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A conical paper cup has a radius of 2 inches. Approximate, to the nearest degree, the angle β (see the figure) so that the cone will have a volume of 60 in3.

β = °

Verified Answer :

I don't know where the angle β is, so I will make the assumption that tanβ = h/r
\(V = \frac{1}{3} \pi r^{2} h\)

V volume = 60
r radius = 2
h = r tanβ

\(tan \beta = \frac{3V }{ \pi r^{3} } = \frac{ 180}{25,1} = 7,17 \\ \\ \beta = 82\)

abidemiokin

The angle β (see the figure) so that the cone will have a volume of 60 in3 is 82.05 degrees

Volume of a cone

The formula for calculating the volume of a cone is expressed as:

V = 1/3πr²h

where

r is the radius

h is the height

Given the following

volume = 60

radius = 2

h = r tanβ

Substitute

V = 1/3πr²(r tanβ)

Substitute

60 = 1/3(3.14)(2)³tanβ

180 = 25.12tanβ

tanβ = 180/25.12

β = 82.05 degrees

Hence the angle β (see the figure) so that the cone will have a volume of 60 in3 is 82.05 degrees

Learn more on volume of cone here: https://brainly.com/question/13677400

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