Question

determine the volume of a comical tin having radius of the base as 30cm and its slant height bad 50cm Find its total surface area take
$\pi$
22 / 7

Answer 1

Radius of the conical tin(r) = 30 cm

Slant Height of the conical tin (l) = 50 cm

Height of the cylinder = h

${l}^{2} = {h}^{2} + {r}^{2}$

${50}^{2} = {h}^{2} + {30}^{2}$

$2500 = {h}^{2} + 900$

$2500 - 900 = {h}^{2}$

$1600 = {h}^{2}$

$h = \sqrt{1600}$

$h = 40 \: cm$

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

$= \frac{1}{3} \times \frac{22}{7} \times {30}^{2} \times 40$

$= \frac{1}{3} \times \frac{22}{7} \times 900 \times 40$

$= \frac{22}{7} \times 300 \times 40$

$= \frac{22}{7} \times 1200$

$= \frac{264000}{7}$

Volume of the conical tin = 37714.2857 cm³

$\tt{\large{\boxed{Total\: Surface\:Area\:of\: the\:cone=\pi r(l+r)}}}$

$= \frac{22}{7} \times 30(50 + 30)$

$= \frac{22}{7} \times 30 \times 80$

$= \frac{22}{7} \times 2400$

$= \frac{52800}{7}$

Total Surface Area of the conical tin = 7542.85714 cm²