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MATH / A solid sphere of ice with radius 4 is placed on a hollow cone (vertex pointed…

Problem

Answer published by the source. Consult the official source to check your work against its answer.

problem

A solid sphere of ice with radius 4 is placed on a hollow cone (vertex pointed down) of radius 4 and height 5. When the ice melts, how much of the water will overflow the cone? Express your answer as a common fraction in terms of π\pi. (For this problem, we ignore the fact that the volume of water decreases when it melts.)
Plain-text mathematical notation (without MathML)
A solid sphere of ice with radius 4 is placed on a hollow cone (vertex pointed down) of radius 4 and height 5. When the ice melts, how much of the water will overflow the cone? Express your answer as a common fraction in terms of π. (For this problem, we ignore the fact that the volume of water decreases when it melts.)
Original LaTeX notation
A solid sphere of ice with radius 4 is placed on a hollow cone (vertex pointed down) of radius 4 and height 5. When the ice melts, how much of the water will overflow the cone? Express your answer as a common fraction in terms of $\pi$. (For this problem, we ignore the fact that the volume of water decreases when it melts.)

level

Level 3

type

Geometry

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Source and history

task_id
5a6b9903-ce96-55e3-8342-17a2e4f08415
task_key
geometry--test--5a6b9903-ce96-55e3-8342-17a2e4f08415
task_revision_id
1
config / split
geometry / test

Official source

initial import