Question

The base of a cone with radius 15 cm and slant height 25 cm is hemispherical.Find the volume of this solid
(p = 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:

$\sf{\implies Volume\;of\;cone=\dfrac{1}{2} \pi r^{2}h}$

$\sf{\implies Volume\;of\;hemisphere=\dfrac{2}{3}\pi r^{3}}$

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

$\sf{\implies Now,\;volume\;of\;cone=\dfrac{1}{3}\pi r^{2}h}$

$\sf{\implies Volume\;of\;cone=\dfrac{1}{3}\times 3.14\times 15\times 15\times 20}$

$\sf{\implies Volume\;of\;cone=4710\;cm^{3}}$

$\sf{\implies Now, volume\;of\;hemisphere=\dfrac{2}{3}\pi r^{3}}$

$\sf{\implies Volume\;of\;hemisphere=\dfrac{2}{3}\times 3.14\times 15\times 15\times 15}$

$\sf{\implies Volume\;of\;hemisphere=7065\;cm^{3}}$

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.

Answer 2

Answer:

⟹Volumeofcone=

2

1

πr

2

h

\sf{\implies Volume\;of\;hemisphere=\dfrac{2}{3}\pi r^{3}}⟹Volumeofhemisphere=

3

2

πr

3

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

\sf{\implies Now,\;volume\;of\;cone=\dfrac{1}{3}\pi r^{2}h}⟹Now,volumeofcone=

3

1

πr

2

h

\sf{\implies Volume\;of\;cone=\dfrac{1}{3}\times 3.14\times 15\times 15\times 20}⟹Volumeofcone=

3

1

×3.14×15×15×20

\sf{\implies Volume\;of\;cone=4710\;cm^{3}}⟹Volumeofcone=4710cm

3

\sf{\implies Now, volume\;of\;hemisphere=\dfrac{2}{3}\pi r^{3}}⟹Now,volumeofhemisphere=

3

2

πr

3

\sf{\implies Volume\;of\;hemisphere=\dfrac{2}{3}\times 3.14\times 15\times 15\times 15}⟹Volumeofhemisphere=

3

2

×3.14×15×15×15

\sf{\implies Volume\;of\;hemisphere=7065\;cm^{3}}⟹Volumeofhemisphere=7065cm

3

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.