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Question

# A solid right circular cone of height 120 cm and radius 60 cm is placed in a right circular cylinder full of water of height 180 cm such that it touches the bottom . Find the volume of water left in the cylinder , if the radius of the cylinder is equal to the radius of te cone .

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Solution

## Height of the cone, h = 120 cm Radius of the cone, r = 60 cm Height of the cylinder, H = 180 cm Radius of the cylinder, R = 60 cm Volume of the cylinder = ${\mathrm{\pi R}}^{2}\mathrm{H}=\mathrm{\pi }{\left(60\right)}^{2}×180{\mathrm{cm}}^{3}$ Volume of the cone = $\frac{1}{3}{\mathrm{\pi r}}^{2}\mathrm{h}=\frac{1}{3}\mathrm{\pi }{\left(60\right)}^{2}×120$ Volume of water left in the cylinder = Volume of cylinder − volume of the cone $=\mathrm{\pi }{\left(60\right)}^{2}×180-\frac{1}{3}\mathrm{\pi }{\left(60\right)}^{2}×120\phantom{\rule{0ex}{0ex}}=\mathrm{\pi }{\left(60\right)}^{2}\left[180-40\right]\phantom{\rule{0ex}{0ex}}=\mathrm{\pi }×3600\left[140\right]\phantom{\rule{0ex}{0ex}}=1584000{\mathrm{cm}}^{3}\phantom{\rule{0ex}{0ex}}=1.584{\mathrm{m}}^{3}$

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