Question

Curved surface area of a cone is 308 sq cm and its slant height is 14 cm. Find the radius of the base

2 cm

3 cm

5 cm

7 cm

​

Answer 1

• Fourth option is correct. Radius is 7 cm.

Step-by-step explanation:

Given:-

• Curved surface area of cone is 308 cm².
• Slant height is 14 cm.

To find:-

• Radius of base.

Solution:-

We know,

Curved surface area of cone = πrl

Where,

• r is radius and l is slant height of cone.

Put r and l in formula :

$\longrightarrow$ 308 = 22/7 × r × 14

$\longrightarrow$ 308 × 7 = 308 × r

$\longrightarrow$ 2156 = 308 × r

$\longrightarrow$ r = 2156/308

$\longrightarrow$ r = 7

Verification:-

$\longrightarrow$ 308 = 22/7 × r × 14

• Put r = 7

$\longrightarrow$ 308 = 22/7 × 7 × 14

$\longrightarrow$ 308 = 2156/7

$\longrightarrow$ 308 = 308

$\boxed{ \sf Hence \: Verified.}$

Therefore,

Radius of base is 7 cm.

Thus, Fourth option is correct.

Answer 2

Answer:

Given :-

• CSA of cone = 308 cm².
• Slanght height = 14 cm

To Find :-

Radius of its base

Solution :-

As we know that

CSA of cone = πrl

Here,

π = 22/7 or 3.14

r = Radius

l = Slanght height

$\sf \:308 = \dfrac{22}{7} \times r \times 14$

$\sf \: 308 = 22 \times r \times 2$

$\sf \: 308 = 44r$

$\sf \: r = \dfrac{308}{44}$

$\sf \: r = 7$

Let's verify

$\sf \: 308 = \dfrac{22}{7} \times 7 \times 14$

$\sf \: 308 = 22 \times 1 \times 14$

$\sf \: 308 = 308$

Hence verified.

$\sf \bigcirc \: 2 \: cm$

$\bigcirc \sf \: 3 \: cm$

$\sf \bigcirc \: 5 \: cm$

$\sf \bigodot \: 7 \: cm$