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314.
A conical tent is to accommodate 11 persons. Each person must have 4 square metre of the space on the ground and 20 cubic metres of air to breath. Find the height of the cone.

Let the base radius and the height of the cone be r cm and h cm respectively. Then,

space space space space space space space space space space space space space space space space space πr squared equals 11 cross times 4 rightwards double arrow space space space space space space space space space space space space space space 22 over 7 straight r squared equals 44 rightwards double arrow space space space space space space space space space space space space space space space straight r squared equals 14 space space space space space space space space space space space space space space space space space space space space... left parenthesis 1 right parenthesis and comma space space space space space space space space space space space space space 1 third πr squared straight h equals 11 cross times 20 rightwards double arrow space space space space space space space space space space space space space space space space 1 third.22 over 7.14. straight h equals 220 space space space space space space space space space space space space space space space vertical line From space left parenthesis 1 right parenthesis rightwards double arrow space space space space space space space space space space space space space space space space space straight h space equals space 15 space straight m space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space.. left parenthesis 2 right parenthesis

Hence, the height of the cone is 15 m.

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315. A conical vessel whose internal radius is 5 cm and height 63 cm is full of oil. Find the the volume of the oil. If that oil is emptied into a cylindrical vessel with internal radius 10 cm, find the height of the oil in the cylindrical vessel.

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316. A semi-circular sheet of metal of diameter 28 cm is bent to form an open conical cup. Find the capacity of the cup.

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317. Find the volume of the largest right circular cone that can be placed in a cube of edge 7 cm.

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318. Bhavya has a piece of canvas whose area is 552 m². She uses it to make a conical tent with a base radius of 7 m. Assuming that all the stiching margins and the wastage incurred while cutting amounts to approximately 2 m², find the volume of the tent that can be made with it.

open parentheses Take space straight pi equals 22 over 7 close parentheses

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319. The height and the slant height of a cone are 21 cm and 28 cm respectively. Find the volume of the cone.

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320. Monica has a piece of canvas whose area is 551 m². She uses it to have a conical tent made, with a base radius of 7 m. Assuming that all the stitching margins and the wastage incurred while cutting, amounts to approximately 1 m², find the volume of the tent that can be made with it.

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