Question

The height of a cone is 15 cm. If its volume is 1570 cm3

, find the radius of the base.​

Answer 1

Answer:

6cm (approx.)

Explanation :

We know that,

$\bigstar \sf Volume \: of \: a \: cone \: is = \pi r^2\dfrac{\boldsymbol h}{3}$

We are given with,

• r(radius) = 15cm.
• Volume = 1570cm³
• Taking $\pi$ as $\sf {3.14}$

Substituting the given values :

$\sf \implies 1570 = \pi {r}^{2} \dfrac{\boldsymbol h}{3}$

$\sf \implies 1570 = 3.14 \times {15}^{2} \times \dfrac{{\boldsymbol h}}{3}$

$\sf \implies \dfrac{1570 }{3.14} = 15 \times 15 \times \dfrac{\boldsymbol h}{3}$

$\sf \implies 500 = 15 \times 5\boldsymbol h$

$\sf \implies 500 = 75\boldsymbol h$

$\sf \implies \frac{500}{75} = \boldsymbol h$

$\sf \implies 6.66 = \boldsymbol h$

$\sf \implies \boldsymbol h \approx 6cm.$

${\underline{\sf {\therefore{ The \: height \: is \: 6cm (approx.)}}}}$

Answer 2

Given:-

• The height of cone is 15 cm.
• Its volume is 1570 cm³.

To Find:-

• Radius of it's base?

Solution:-

Volume of cone

$\dag { \boxed{ \underline{ \pink{⅓ \times \rm \pi \times {r}^{2} \times h}}}}$

Where,

• r = radius
• h = height

According to the question:-

$↝\frac{1}{3} \times \rm \pi \times {r}^{2} \times h = 1570 \\ \\ ↝ \cancel\frac{1}{3} \times \rm 3.14 \times {r}^{2} \times \cancel{15} = 1570 \\ \\ ↝ 3.14\times {r}^{2} \times 5 = 1570 \\ \\↝ {r}^{2} = \frac{1570}{3.14 \times 5} \\ \\↝ {r}^{2} = \cancel \frac {1570}{15.70} \\ \\ ↝{r}^{2} = 100 \\ \\ ↝r = \sqrt{100} \\ \\↝ \dag {\boxed {\blue{ r = 10}}}$

Hence, the radius of base is 10 cm.