Question

A hemispherical pond is filled with 523.908 m³ of water. Find the maximum depth of pond.

Answer 1

We know, volume of hemisphere (v)=$\frac{2}{3} \pi r^{3}$

where, r is radius and can be given as $r = \frac{3v}{2\pi}^{\frac{1}{3}}$

hence, r = 6.301 m

where, $523.908m^{3}$

for maximum depth radius of hemisphere will be equal to depth of pond

hence, h = 6.301 m

Answer 2

GIVEN :

Volume of the hemispherical pond = 523.908 m³

Let the maximum depth (radius) = r m

Volume of the hemisphere = ⅔ πr³

523.908 = ⅔ (22/7) × r³

r³ = (523908 × 3 × 7)/ (1000 × 2 ×22)

r³ = (11907 ×21)/1000

r³ = (3× 3 × 3 × 3 × 3 × 7 × 7 × 7× 3) /1000

r³ =( 3× 3 × 3 × 3 × 3 ×3× 7 × 7 × 7) /1000

r³ = 3³ × 3³ × 7³/ 10³

r = 3 × 3 × 7 /10 = 63/10 = 6.3 m

Hence the maximum depth of the hemispherical pond is 6.3 m

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