Question

The base of a cone with radius 15 cm and slant height 25 cm is hemispherical. Find
I the volume of this solid. (n = 3.14)​

Answer 1

Solution:

Given:

⇒ Radius of cone (r) = 15 cm

⇒ Slant Height of cone (l) = 25 cm

to find :  

⇒ Volume of solid

Formula used:

=>volume of  cone = 1/2πr².h

=>volume of hemisphere = 2/3πr³

Now, firstly we will find the height of the cone by Pythagoras theorem.

⇒ l² = r² + h²

⇒ 25² = 15² + h²

⇒ 625 = 225 + h²

⇒ 625 - 225 = h²

⇒ 400 = h²

⇒ h = ±20

⇒ h = 20 cm

==>Now volume of cone = 1/3πr².h

=>volume of cone = 1/3 *3.14 * 15 * 15 * 20

=>volume of cone = 4710cm³

==> Now , volume of hemisphere = 2/3πr³

=>volume of hemisphere = 2\3 * 3.14 * 15 * 15 * 15

=> volume of hemisphere = 7065cm³

Now, total volume of solid = Vol. of cone + Vol. of hemisphere

⇒ Total volume = 4710 + 7065

⇒ Total volume = 11775 cm³

Hence, volume of solid is 11775 cm³

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