Question

The height of a cone is 15 cm. if it's volume is 500π cm^3, then find the radius of it's base​

Answer 1

$\\ \\ \large\underline{ \underline{ \sf{ \red{given:} }}}$

• Volume of cone is 500π³ cm³.

• Height of cone is 15cm.

$\\ \\ \large\underline{ \underline{ \sf{ \red{to \: find:} }}}$

• Radius of base of the cone.

$\\ \\ \large\underline{ \underline{ \sf{ \red{solution:} }}}$

$\\ \bigstar \boxed{ \bf \:volume \: of \: cone = \frac{1}{3}\pi \: {r}^{2} h }$

Here ,

• Volume of cone = 500πcm³

• r = ?

• h = 15cm

Putting values , we get...

$\\ \sf \: 500\pi = \frac{1}{ \cancel3} \pi \: {r}^{2} ( \cancel{15}) \\ \\ \sf \: 500 \cancel\pi = \cancel\pi \: {r}^{2} (5) \\ \\ \sf \: 500 = {r}^{2} (5) \\ \\ \sf \: {r}^{2} = \frac{500}{5} \\ \\ \sf \: {r}^{2} = 100 \\ \\ \boxed{ \sf \: \pink{ r = 10cm}}$

Hence , radius of base is 10cm.

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More to know :-

→ T.S.A of cone = πr(r+l)

→ C.S.A of cone = πrl

Here ,

• r = radius of base
• l = slant height
• h = height of cone

Answer 2

Answer :

$\large \implies \mathbb{ r = 10 cm}$

Solution :

Given :

• Height of a cone, h = 15 cm.
• Volume of cone = 500π cm³.

To Find :

• Radius of it's base .

Lets solve ,

$\large \bigstar \boxed{\tt Volume \; of \: the \: cone = \frac{1}{3}\pi r^2 h}$

Putting the values ,

$\implies 500\pi = \frac{1}{3}\: \pi \: r^2 \: 15 \\ \\ \sf \implies 500 \pi= \frac{1}{\cancel{3}} \: \pi \: r^2 \: \cancel{3}×5 \\ \\ \implies \sf 500\cancel{\pi} = r^2 \: \cancel{\pi} \: 5 \\ \\ \sf \implies r^2 = \frac{500}{5} \\ \\ \sf \implies r^2 = 100 \\ \\ \implies \underline{\boxed{\mathbb r = 10cm}}$

Therefore,

Radius of the base of circle is 10 cm.