Question

a right circular cone
of height 4cm has a CSA 47.1cm² find it's volume
(3.14)​

Answer 1

Step-by-step explanation:

Given=》

height of the cone h = 4cm

Curved surface area =47.1cm²

To find =》

Volume =?

Solution =》

Let r is the radius and l is the slant height of the circular cone.

Again given curve surface = 47.1

=》πrl= 47.1

$3.14 \times r \times \sqrt{r {}^{2} + h {}^{2} } = 47.1 \\ = r \times \sqrt{r {}^{2} + h {}^{2} } = \frac{47.1}{3.14} \\ = r {}^{} \times \sqrt{r {}^{2} { + h {}^{} }^{2} } = 15 \\ = r \times \sqrt{r {}^{2} + {4}^{2} } = 15 \\ = r \times \sqrt{r {}^{2} + 16} = 15 \\ = r { \times}^{} (r {}^{2} + 16) = 15 {}^{2} \\ = r {}^{2} \times (r {}^{2} + 16) = 225 \\ = r {}^{4} + 16r {}^{2} - 225 = 0 \\ = (r {}^{2} - 9)(r {}^{2} + 25) = 0 \\ = r {}^{2} = 9. - 25$

Since r2 ≠ -25

so r²=9

r=3

Vol of cone = π r²h/3

$\frac{3.14 \times 3 \times 3 \times 4}{3} \\ = 3.14 \times 3 \times 4 \\ = 3.14 \times 12 \\ = 37.68cm {}^{3}$

So , the volume is 37.68cm³