Question

CSA of a cone = 308cm^2
slant height= 14cm
Find I) radius
ii) total surface area​

Answer 1

To Find : --

• (i) Radius
• (ii) Total Surface Area of cone

Solution : --

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

Curved surface area of cone = πrl

›› πrl = 308

›› πr × 14 = 308

››( 22/7 ) × r × 14 = 308

›› 22r × 2 = 308

›› 44r = 308

›› r = 308/44

›› r = 7

• Radius of cone = 7cm

As we know that,

Total Surface Area of cone = πr(r + l)

= 22/7 × 7(7 + 14)

= 22(21)

= 462cm²

• Total surface area of cone is 462cm²

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Answer 2

i) For radius:

Curved surface area of cone = πrl

Substitute the known values,

→ 22/7 × r × 14 = 308

→ 22/7 × r = 308/14

→ 22/7 × r = 22

→ r = 22 × 7/22

→ r = 7

Hence, the radius of the cone is 7 cm.

ii) For total surface area:

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

Substitute the known values,

→ 22/7 × 7(7 + 14)

→ 22(21)

→ 462

Hence, the total surface area of the cone is 462cm².