A solid right come of diameter 14 cm and height 8 cm is melted to form a hollow sphere, if the external diameter of the sphere is 10 cm, find the internal diameter of the sphere.

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Solution

d = 14, r = 7cm
h = 8 cm
Volume of the cone = $\frac{1}{3} π r^{2} h$
= $\frac{1}{3} \times \frac{22}{7} \times 7 \times 7 \times 8$
= $410.66 c m^{3}$
external radius = R = 5cm
internal radius = r = ?
$\frac{4}{3} \times \frac{22}{7} (R^{3} - r^{3}) = 410.66$
$(125 - r^{3}) = \frac{410.66 \times 21}{88}$
$125 - r^{2} = 97.998$
$r^{3} = 125 - 97.998$
$r^{3} = 27.0015 = r ≅ 3$
internal diameter = 6 cm.

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A solid right come of diameter 14 cm and height 8 cm is melted to form a hollow sphere, if the external diameter of the sphere is 10 cm, find the internal diameter of the sphere.

d = 14, r = 7cm h = 8 cm Volume of the cone = 13πr2h = 13×227×7×7×8 = 410.66 cm3 external radius = R = 5cm internal radius = r = ? 43×227(R3−r3)=410.66 (125−r3)=410.66×2188 125−r2=97.998 r3=125−97.998 r3=27.0015=r≅3 internal diameter = 6 cm.