Question

The curved surface area of a cone is 12320 sq. cm, if the radius of its base is 56 cm, find its height. *

42 cm

44 cm

40 cm

46 cm

​

Answer 1

Answer :

›»› The height of the cone is 42 cm.

Given :

• The curved surface area of a cone is 12320 sq. cm, if the radius of its base is 56 cm.

To Find :

• Height of the cone = ?

Solution :

Let us assume that, the Slant height of a cone is x cm.

As we know that

→ CSA of cone = πrl

→ 12320 = πrl

→ 12320 = 22/7 * 56 * x

→ 12320 = 22 * 8 * x

→ 12320 = 176 * x

→ 12320 = 176x

→ x = 12320 ÷ 176

→ x = 70

The length of the cone is 70 cm.

Now,

As we know that

→ l² = h² + r²

→ (70)² = h² + (56)²

→ 4900 = h² + (56)²

→ 4900 = h² + 3136

→ 4900 - 3136 = h²

→ h² = 1764

→ h = √1764

→ h = 42

Hence, the height of the cone is 42 cm.

Answer 2

Given :

• Curved Surface Area of Cone is 12320 cm² .
• Radius of Cone is 56 cm .

To Find :

• Height of Cone .

Solution :

Firstly we will Find Slant Height :

Using Formula :

$\longmapsto\tt\boxed{C.S.A\:of\:Cone=\pi{rl}}$

Putting Values :

$\longmapsto\tt{12320=\dfrac{22}{{\cancel{7}}}\times{{\cancel{56}}}\times{l}}$

$\longmapsto\tt{12320=176\:l}$

$\longmapsto\tt{l=\cancel\dfrac{12320}{176}}$

$\longmapsto\tt\bf{l=70\:cm}$

Now ,

For Height :

$\longmapsto\tt\bf{h=\sqrt{{(l)}^{2}-{(r)}^{2}}}$

$\longmapsto\tt{h=\sqrt{{(70)}^{2}-{(56)}^{2}}}$

$\longmapsto\tt{h=\sqrt{4900-3136}}$

$\longmapsto\tt{h=\sqrt{1764}}$

$\longmapsto\tt\bf{h=42\:cm}$

So , The Height of Cone is 42 cm .

Option a) 42 cm is Correct ..