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If the height and slant height of a cone...

If the height and slant height of a cone are 6 cm and 10 cm respecitvely. Then determine the total surface area and the volume of the cone.

Text Solution

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The height of the right circular cone is 6cm and its slant height is 10 cm .
Let the radius of the cone be r cm.
`therefore 6^2+r^2=10^2rArr r^2=100-36=64rArr r=sqrt(64)=8`.
`therefore` the radius of the cone is 8 cm .
`therefore` the total surface area of the cone `=pi xx 8(8+10)sq-cm=(22)/(7)xx8xx18sq-cm=144pi sq-cm`.
Again , the volume of the cone `=(1)/(3)pi xx (8)^2xx6` cubic - cm `=128pi` cubic - cm.
Hence the total surface ara of the cone `=144pi ` sq-cm and volume `=128pi`cubic -cm.
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