Question

the radius of the base and the height of the right sercular cone are 9cm and 8cm respectively find the volume of total surface area by using formula 1/3πr2h
​

Answer 1

Given -

• The radius (r)of the right circular cone= 9cm
• Height (h) of the right circular cone=8cm

To find -

• Volume of the cone
• Total surface area (T. S. A) of cone

Solution -

We know that,

$volume \: of \: the \: cone = \frac{1}{3} \pi {r}^{2} h$

By putting the values we will get -

$Volume \: of \: the \: cone = \frac{1}{3} \times \frac{22}{7} \times {(9)}^{2} \times 8$

$Volume \: of \: the \: cone = \frac{4752}{7}$

$Volume \: of \: the \: cone = 678.9$

Therefore the volume of the cone is 678.9 cm³

Now,

To find total surface of the cone, first we need to

find the slant height (l) of the cone

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

$l = \sqrt{ {(9)}^{2} + {(8)}^{2} }$

$l = \sqrt{81 + 64}$

$l = \sqrt{145}$

$l = 12.04$

We know that,

$T. S. A\: of \: cone = \pi \: r(l + r)$

By putting the values we will get -

$T. S. A\: of \: cone = \frac{22}{7} \times 9(12.04 + 9)$

$T. S. A\: of \: cone = \frac{198}{7} \times 21.04$

$T. S. A\: of \: cone = \frac{4165.92}{7}$

$T. S. A\: of \: cone = 595.13$

Therefore total surface of the cone is 595.13 cm²