Find the volume of a cone, if its total surface area is 7128 sq.cm and radius of base is 28 cm. ( π = 22/7)

Question

Find the volume of a cone, if its total surface area is 7128 sq.cm and radius of base is 28 cm. ( π = \(\frac{22}7\))

Answer 1

Given: Radius (r) = 28 cm, 

Total surface area of cone = 7128 sq.cm 

To find: Volume of the cone

Solution:

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

∴ 7128= y x 28 x (l + 28) 

∴ 7128 = 22 x 4 x(l +28) 

∴ l + 28 = \(\frac{7128}{22\,\times\,4}\)

∴ l + 28 = 81 

∴ l = 81 – 28 

∴ l = 53cm

ii. Now, l² = r² + h² 

∴ 53² = 28² + h² 

∴ 2809 = 784 + h 

∴ 2809 – 784 = h² 

∴ h² = 2025 

∴ h = \(\sqrt{2025}\)…… [Taking square root on both sides] 

= 45 cm

= 22 x 4 x 28 x 15 

= 36960 cubic.cm 

∴ The volume of the cone is 36960 cubic.cm.