Question

Curved surface area of a cone is 308 cm² and slant height 14 cm ,find
A radius
B total surface area
C volume​

Answer 1

Given -

• Slant Height of cone = 14 cm

• Curved surface area of cone = 308 cm²

To find -

• Radius

• Total surface area

• Volume

Solution -

Let the radius of cone be 'r'

Curved surface area of cone = πrl

On substituting the values -

CSA of cone = πrl

308 = 22/7 × r × 14

308 = 44 × r

r = 308/44

→ r = 7cm

$\therefore$ Radius of cone is 7cm

ii) Total surface area of cone = πr(l + r)

where,

π = 22/7

r = Radius

l = slant Height

On substituting the values -

TSA of cone = πr(l + r)

TSA of cone = 22/7 × 7 (14 + 7)

TSA of cone = 22(21)

TSA of cone → 462cm³

$\therefore$ Total surface area of cone is 462cm³

iii) Volume of cone = 1/3πr²h

On substituting the values -

Volume of a cone = 1/3 πr²h

= 1/3 × 22/7 × 7² × 14

= 1/3 × 22/7 × 49 × 14

= 22/21 × 49 × 14

= 15092/21

→ 718.66

$\therefore$ Volume of cone is 718.66

____________________________________________

Answer 2

Given :-

CSA of cone = 308 cm²

Slant height = 14 cm

To Find :-

❶ Radius

❷ TSA of cone

❸ Volume

Diagram

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Solution :-

❶ Radius

Let the radius be 'r'

As we know that

$\bf \: CSA \: of \: cone \: = \pi rl$

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

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

$\sf \: 308 = 44r$

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

Radius of cone = 7 cm

❷ TSA of cone

As we know that

$\bf \: TSA \: of \: cone = \pi \: r(l + r)$

$\sf \: TSA \: of \: cone \: = \dfrac{22}{7} \times 7(14 + 7)$

$\sf \: TSA \: of \: cone \: = 22(21)$

Total surface area of cone is 462cm³.

❸ Volume of Cone

As we know that

$\sf \: volume \: of \:cone = \dfrac{1}{3} πr²h$

$\sf \: volume \: = \dfrac{1}{3} \times \dfrac{22}{7} \times {7}^{2} \times 14$

$\sf \: volume \: = \dfrac{1}{3} \times \dfrac{22}{7} \times 49 \times 14$

$\sf \ \dfrac{22}{21} \times 14 \times 49$

$\sf \: volume \: = \dfrac{15092}{21}$

Volume of Cone = 718.66 cm.