Question

A conical tent has the area of its base as 154 m2 and that of its curved surface area as 550 m2. Find the volume of the tent.

Answer 1

base area = 154 square metres
$\pi {r}^{2} = 154$
${r}^{2} = 154 \times 7 \div 22$
${r}^{2} = 49$
$r = 7$
CSA = 550 square metres
$\pi \: rl = 550$
$l = 550 \times 7 \div (22 \times 7)$
$l = 25$
${h}^{2} = {l}^{2} - {r}^{2}$
$= 625 - 49$
$= 576$
$h = 24$
$volume \: = \frac{1}{3} \pi {r}^{2} h$
$= \frac{1}{3} \times 154 \times 24$
$= 1232 \: cubic \: meters$

Answer 2

Answer:

1232 m3

Step-by-step explanation:

Area of the base = 154 m2

Pi * r2 = 154

22/7 * r2 = 154

r2 = 154 * 7/22

r2 = 49

radius = 7

Now,

CSA OF CONE = Pi * r * l

550 m2 = 22/7 * 7 * l

l= 550/22

l= 25 m

h = root of l2 - r2

h= root of 625 - 49

h = root of 576

h= 24 m

Volume = 1/3 *Pi * r2 * h

= 1/3 * 22/7 * 49 * 24

= 1232 m3

Hope this helps ❤