Mathematics

Find the maximum volume of a cone that can be carved out of a solid hemisphere of radius r cm.

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Answer

The max height and radius of cone, inside a hemisphere of radius r cm can be r cm.

A vessel is in the form of an inverted cone. Its height is 8 cm and the radius of the top which is open is 5 cm. It is filled with water up to the rim. When lead shots, each of which is a sphere of radius 0.5 cm, are dropped into the vessel, one-fourth of the water flows out. Find the number of lead shots dropped in the vessel. Cylinder, Cone, Sphere, Concise Mathematics Solutions ICSE Class 10.

Volume of cone = $\dfrac{1}{3}πr^2h$

= $\dfrac{1}{3} \times π \times r^2 \times r$

= $\dfrac{1}{3}πr^3 \text{ cm}^3.$

Hence, maximum volume of cone that can be carved out of solid hemisphere of radius r cm = $\dfrac{1}{3}πr^3$ cm³.

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A vessel is in the form of an inverted cone. Its height is 8 cm and the radius of the top which is open is 5 cm. It is filled with water up to the rim. When lead shots, each of which is a sphere of radius 0.5 cm, are dropped into the vessel, one-fourth of the water flows out. Find the number of lead shots dropped in the vessel.
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