A clay ball was split in half and its insides is scooped out. If the hollow shape formed is a hemisphere of radius 7 cm, and has a thickness of 2 cm. Find the volume of the clay remaining in both the halves.

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Solution

Radius of hemisphere = 7 cm

Thickness of the clay ball = 2 cm

Radius of the clay ball = 7 + 2 = 9 cm

Volume of clay ball remaining is =

$\frac{4}{3} π {r_{1}}^{3} - \frac{4}{3} π {r_{2}}^{3} \frac{4}{3} π [9^{3} - 7^{3}] \frac{4}{3} \times \frac{22}{7} \times 386 = 1617.52 c m^{3}$

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[U s e π = \frac{22}{7}]

From each end of a solid metal cylinder, metal was scooped out in hemispherical form of same diameter. The height of the cylinder is $10 c m$ and its base is of radius $4.2 c m$ . The rest of the cylinder is melted and converted into a cylindrical wire of $1.4 c m$ thickness. Find the length of the wire.

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A clay ball was split in half and its insides is scooped out. If the hollow shape formed is a hemisphere of radius 7 cm, and has a thickness of 2 cm. Find the volume of the clay remaining in both the halves.

Radius of hemisphere = 7 cm Thickness of the clay ball = 2 cm Radius of the clay ball = 7 + 2 = 9 cm Volume of clay ball remaining is = 43πr13−43πr2343π[93−73]43×227×386=1617.52 cm3

Radius of hemisphere = 7 cm

Thickness of the clay ball = 2 cm

Radius of the clay ball = 7 + 2 = 9 cm

Volume of clay ball remaining is =

$\frac{4}{3} π {r_{1}}^{3} - \frac{4}{3} π {r_{2}}^{3} \frac{4}{3} π [9^{3} - 7^{3}] \frac{4}{3} \times \frac{22}{7} \times 386 = 1617.52 c m^{3}$