Question

find the volume of a cone, if it's total surface area is 7128 sq.cm and radius of base is 28 cm. (π=22/7)​

Answer 1

Answer:

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Answer 2

Answer:

Volume of cone = 36960 cm³

Step-by-step explanation:

Given :

Total surface area of cone(T.S.A.) = 7128 cm²

Radius of cone = 28 cm

Find :

The volume of a cone

Solution :

Total surface area of cone =

⇒ π r ( l + r ) = 7128

⇒ 22/7 × 28 ( l + 28 ) = 7128

⇒88 ( l + 28 ) = 7128

⇒ l + 28 = 7128 / 88

⇒ l + 28 = 81

⇒ l = 81 - 28 = 53 cm

⇒ l = 53 cm

Now,

To find height

$\sf{h= \sqrt{l^2-r^2} \\ \sf{h=\sqrt{53^2-28^2}}\\ \sf{h=\sqrt{2025}}\\ \sf{h=45cm}}}$

• Volume of cone = (1/3) π r²h

⇒ 1 / 3 × (22/7) × 28 × 28 × 45

⇒ 36960

Volume of cone = 36960 cm³