Question

the diameter of the base of a right circular cone is 21 cm and its height is 14cm .its curved surface area is​

Answer 1

Answer :-

Given :

Diameter of the base of right circular cone = 21 cm

Height = 14 cm

To find :

The curved surface area of the right circular cone.

Solution :

$\sf Radius \: of \: the \: right \: circular \: cone \: = \: \dfrac{21}{2} \: cm \: = \: 10.5 \: cm$

Let's find the slant height (l) of the right circular cone first.

$\boxed{\sf Slant \: height = \: \sqrt{ {r}^{2} + {h}^{2} }}$

$\sf\longrightarrow \sqrt{ {10.5}^{2} + {14}^{2} }$

$\sf\longrightarrow \sqrt{ 110.25 + 196 }$

$\sf\longrightarrow \sqrt{ 306.25 }$

$\sf\longrightarrow 17.5$

.°. The slant height of the cone = 17.5 cm

Now, We know that,

$\boxed{\sf Curved \: surface \: area \: of \: cone \: = \: \pi \times r \times l}$

[where r = radius and l = slant height of the cone]

$\sf\longrightarrow \dfrac{22}{7} \times 10.5 \times 17.5$

$\sf\longrightarrow \dfrac{22}{7} \times \dfrac{105}{10} \times \dfrac{175}{10}$

$\sf\longrightarrow 577.5$

Hence, the curved surface area of the right circular cone is 577.50 cm²

Answer 2

Answer:

Given :-

• The diameter of the base of a right circular cone is 21 cm and it's height is 14 cm.

To Find :-

• What is the curved surface area.

Formula Used :-

➦ By using Pythagoras Theorem we know that,

★ ${\red{\boxed{\small{\bold{{(Slant\: Height)}^{2} =\: {(Radius)}^{2} + {(Height)}^{2}}}}}}$ ★

➦ To find curved surface area or C.S.A of cone we know that,

★ ${\red{\boxed{\small{\bold{C.S.A\: of\: Cone\: =\: {\pi}rl}}}}}$ ★

where,

• r = Radius
• l = Slant Height

Solution :-

First we have to find the radius of a cone,

As we know that,

★ $\sf\boxed{\bold{\small{Radius =\: \dfrac{Diameter}{2}}}}$ ★

Then,

↪ $\sf Radius =\: \dfrac{21}{2}$

➤ $\sf\bold{\green{Radius =\: 10.5\: cm}}$

Again, we have to find the slant height of a cone,

Given :

• Radius = 10.5 cm
• Height = 14 cm

⇒ $\sf {(Slant\: Height)}^{2} =\: {(10.5)}^{2} + {(14)}^{2}$

⇒ $\sf {(Slant\: Height)}^{2} =\: 110.25 + 196$

⇒ $\sf {(Slant\: Height)}^{2} =\: 306.25$

⇒ $\sf Slant\: Height =\: \sqrt{306.25}$

➠ $\sf\bold{\pink{Slant\: Height =\: 17.5\: cm}}$

Hence, slant height of a cone is 17.5 cm.

Now, we have to find the curved surface area of a cone,

Given :

• Radius = 10.5 cm
• Slant height = 17.5 cm

According to the question by using the formula we get,

↦ $\sf C.S.A =\: \dfrac{22}{7} \times 10.5 \times 17.5$

↦ $\sf C.S.A =\: \dfrac{22 \times 105 \times 175}{7 \times 10 \times10}$

↦ $\sf C.S.A =\: \dfrac{2310 \times 175}{70 \times 10}$

↦ $\sf C.S.A =\: \dfrac{\cancel{404250}}{\cancel{700}}$

↦ $\sf C.S.A =\: 577.5$

➠ $\sf\bold{\purple{C.S.A =\: 577.50\: {cm}^{2}}}$

${\underline{\boxed{\small{\bf{\therefore The\: curved\: surface\: area\: of\: a\: cone\: is\: 577.50\: {cm}^{2}\: .}}}}}$