Question

A tap is hemisphere over a cone the common radius is 7 cm, height of the conical part is 24cm find the volume of the top

Answer 1

A top has a conical bottom part and hemispherical upper part.

Radius of hemisphere, r = 7cm

Radius of conical part, r = 7cm

height of conical part , h = 24 cm

Volume of top = volume of cone + volume of hemisphere

$\Rightarrow V = \frac{1}{3} \pi {r}^{2} h + \frac{2}{3} \pi {r}^{3} \\ \\ \Rightarrow V = \frac{1}{3} \pi {r}^{2} (h + 2r) \\ \\ \Rightarrow V = \frac{1}{3} \times \frac{22}{7} \times {7}^{2} \times (24 + 2 \times 7) \\ \\ \Rightarrow V = \frac{22 \times 7}{3} \times 38 \\ \\ \Rightarrow V = 1950.67 \: {cm}^{2}$

Answer 2

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A top has a conical bottom part and hemispherical upper part.

Radius of hemisphere, r = 7cm

Radius of conical part, r = 7cm

height of conical part , h = 24 cm

Volume of top = volume of cone + volume of hemisphere

$\Rightarrow V = \frac{1}{3} \pi {r}^{2} h + \frac{2}{3} \pi {r}^{3} \\ \\ \Rightarrow V = \frac{1}{3} \pi {r}^{2} (h + 2r) \\ \\ \Rightarrow V = \frac{1}{3} \times \frac{22}{7} \times {7}^{2} \times (24 + 2 \times 7) \\ \\ \Rightarrow V = \frac{22 \times 7}{3} \times 38 \\ \\ \Rightarrow V = 1950.67 \: {cm}^{2}$

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