Question

The curved surface area of a right circular cone is 12320 cm². If the radius of its base is 56cm, then find its height.​

Answer 1

EXPLANATION.

Curved surface area of right circular cone = 12320 cm².

Radius of its base = 56 cm.

As we know that,

Formula of :

Curved surface area of cone = πrl.

⇒ h = √(l² - r²).

Using this formula in the equation, we get.

⇒ πrl = 12320.

⇒ 22/7 x 56 x l = 12320.

⇒ 22 x 8 x l = 12320.

⇒ 176 x l = 12320.

⇒ l = 70 cm.

⇒ h = √(l² - r²).

⇒ h = √(70)² - (56)².

⇒ h = √4900 - 3186.

⇒ h = √1714.

⇒ h = 41.400 ≈ 42 cm.

Height of a right circular cone : 42 cm.

                                                                                                                     

MORE INFORMATION.

(1) Volume of cuboid : L x B x H.

(2) Volume of a cone : a³.

(3) Volume of cylinder : πr²h.

(4) Volume of cone : 1/3πr²h.

(5) Volume of hemisphere : 2/3πr³.

(6) Volume of sphere : 4/3πr³.

Answer 2

Answer:

Given :-

• The curved surface area of a right circular cone is 12320 cm².
• The radius of its base is 56 cm.

To Find :-

• What is the height of a cone.

Formula Used :-

$\clubsuit$ Curved Surface Area or C.S.A. of Cone Formula :

$\bigstar \: \: \sf\boxed{\bold{\pink{Curved\: Surface\: Area_{(Cone)} =\: {\pi}rl}}}\: \: \: \bigstar$

where,

• π = Pie or 22/7
• r = Radius
• l = Slant Height

Solution :-

First, we have to find the slant height of cone :

Given :

• Curved Surface Area or C.S.A. of Cone = 12320 cm²
• Radius of its base = 56 cm

According to the question by using the formula we get,

$\implies \bf Curved\: Surface\: Area_{(Cone)} =\: {\pi}rl$

$\implies \sf 12320 =\: {\pi}rl$

$\implies \sf 12320 =\: \dfrac{22}{7} \times 56 \times l$

$\implies \sf 12320 =\: \dfrac{22 \times 56}{7} \times l$

$\implies \sf 12320 =\: \dfrac{1232}{7} \times l$

$\implies \sf 12320 \times \dfrac{7}{1232} =\: l$

$\implies \sf \dfrac{12320 \times 7}{1232} =\: l$

$\implies \sf \dfrac{86240}{1232} =\: l$

$\implies \sf 70 =\: l$

$\implies \sf\bold{\green{l =\: 70}}$

Hence, the slant height of a right circular cone is 70 cm .

Now, we have to find the height of cone :

Given :

• Slant Height = 70 cm
• Radius = 56 cm

According to the question by using the formula we get,

$\implies \bf (l)^2 =\: (r)^2 + (h)^2$

$\implies \sf (70)^2 =\: (56)^2 + h^2$

$\implies \sf (70 \times 70) =\: (56 \times 56) + h^2$

$\implies \sf 4900 =\: 3136 + h^2$

$\implies \sf 4900 - 3136 =\: h^2$

$\implies \sf 1764 =\: h^2$

$\implies \sf \sqrt{1764} =\: h$

$\implies \sf \sqrt{\underline{42 \times 42}} =\: h$

$\implies \sf 42 =\: h$

$\implies \sf\bold{\red{h =\: 42}}$

$\small \sf\bold{\purple{\underline{\therefore\: The\: height\: of\: right\: circular\: cone\: is\: 42\: cm\: .}}}$