Question

7. When you eat an ice cream scoop with a volume of 179.59 cubic inches, find the radius.

Then find the surface area of that scoop. (Normal thoughts of a geometry
ice cream.) *****hint - go backwards****
student eating

Answer 1

We can use the formula for the volume of a sphere to find the radius of the ice cream scoop:

V = (4/3)πr^3

179.59 = (4/3)πr^3

r^3 = 179.59 / (4/3)π

r^3 = 42.99

r = (42.99)^(1/3)

r ≈ 3.4 inches

Now that we know the radius of the ice cream scoop, we can find its surface area. The formula for the surface area of a sphere is:

A = 4πr^2

A = 4π(3.4)^2

A ≈ 145.27 square inches

Therefore, the surface area of the ice cream scoop is approximately 145.27 square inches.

Answer 2

• radius: 3.50 in
• area: 153.9 in²

Explanation:

You want the radius and area of a spherical ice cream scoop with a volume of 179.59 cubic inches.

Volume

The volume of a sphere is given by the formula ...

V = (4/3)πr³

Radius

Then the radius will be ...

r = ∛(3V/(4π))

r = ∛(3·179.59/(4π)) ≈ 3.49997 . . . . in

The radius is about 3.50 inches.

Area

The area of a sphere is given by ...

A = 4πr^2

A ≈ 4π·(3.49997 in)² ≈ 153.9355 . . . . in²

The area of that scoop is about 153.9 square inches.

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Additional comment

A scoop 7 inches in diameter would likely be served in a bowl.

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