volume ratio - 2

Geometry Level 1

If the largest sphere is carved from a wooden cube measuring 10 units on an edge, what is the ratio of the volume of this sphere to the volume of the cube?

Give your answer as a fraction.

Use π = 22 7 \pi=\frac{22}{7} .

9 21 \dfrac{9}{21} 10 21 \dfrac{10}{21} 11 21 \dfrac{11}{21} 12 21 \dfrac{12}{21}

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1 solution

P S
Dec 8, 2017

volume of the sphere: V = 4 3 \frac{4}{3} x Pi x r^3 = 4 3 \frac{4}{3} x 22 7 \frac{22}{7} x 5^3 = 11000 21 \frac{11000}{21}
volume of the cube: V = e^3 = 1000

ratio: V ( s p h e r e ) V ( c u b e ) \frac{V(sphere)}{V(cube)} = 11000 21 \frac{11000}{21} / 1000 1 \frac{1000}{1} = 11000 21000 \frac{11000}{21000} = 11 21 \frac{11}{21}

0 Helpful 1 Interesting 1 Brilliant 1 Confused

Why did we take the radius of the sphere as 5 ?

Shloka Gurav - 2 years, 10 months ago

The height of the cube is 10units. Max diameter of the sphere is, therefore, 10units: r=D/2 = 5units

Nicolas Dambaek - 2 years, 3 months ago

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