Question

aA right circular cone of vertical height 24 CM has volume 616 cm. Find the area of its curved surface .​

Answer 1

Answer:

for cone:

height ,h = 24cm

volume ,V= 616cm³

$\frac{1}{3}\pi \: r^{2}h$

ATQ,

$\frac{1}{3} \times \frac{22}{7} \times {r}^{2} \times 24 = 616cm^{3} \\ {r}^{2} = 24.5 \\ r = 4.9cm$

slant height, L=?

$l = \sqrt{ {h}^{2} + {r}^{2} } \\ l = \sqrt{4.9^{2} + 24 ^{2} } \\ l = \sqrt{600.5} \\ l = 24.5$

now CSA(curved surface area of cone =

$\pi \: rl \\ = \frac{22}{7} \times 4.9 \times 24.5 \\ = 377.3 {cm}^{2}$

and area of cone=

$\pi \: r \: (r + l) \\ \frac{22}{7} \times 4.9(24.5 + 4.9) \\ = 452.76 {cm}^{2}$