What is the radius?

Geometry Level 2

A water tank in the shape of a sphere is 80% full of water. Another water tank in the shape of inverted cone has a radius of 1.5 m and a height of 3 m. All water from the spherical tank was transferred to the inverted conical tank until 100% full. The conical tank cannot accommodate all the water, so an amount of 4.24 m³ overflowed after the transfer. What is the radius of the spherical tank?

1.3 m 1.5 m 1.1 m 1.6 m

A Former Brilliant Member by A Former Brilliant Member

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1 solution

volume of water = volume of cone + volume of water that overflowed after the transfer

let Vw = volume of water

Vc = volume of cone

Vo = volume of water that overflowed after the transfer

Vs = volume of sphere

Vw = Vc + Vo

Vw = 1 3 \frac{1}{3} π r ² h πr²h + 4.24 4.24 = 1 3 \frac{1}{3} π ∗ 1. 5 2 ∗ 3 π*1.5^2*3 + 4.24 4.24 = 11.31 m 3 11.31 m^3

0.8 V s = 11.31 m 3 0.8Vs = 11.31 m^3

0.8 0.8 * 4 3 \frac{4}{3} π π r 3 r^3 = 11.31 m 3 11.31 m^3

r r = 1.5 m 1.5 m

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