From a circular cylinder of diameter 10 cm and height 12 cm, a conical cavity of the same base radius and of the same height is hollowed out. Find the volume and the whole surface of the remaining solid. Leave the answer in π
Mensuration
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Question

From a circular cylinder of diameter 10 cm and height 12 cm, a conical cavity of the same base radius and of the same height is hollowed out. Find the volume and the whole surface of the remaining solid. Leave the answer in π

Mensuration

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KnowledgeBoat · Accepted Answer

Given, Height of the cylinder (H) = 12 cm Radius of the base of the cylinder (R) = = 5 cm Height of the cone (h) = 12 cm Radius of the cone (r) = 5 cm Volume of the remaining part = Volume of cylinder - Volume of cone = πR2H - πr2h ∴ The volume of the remaining solid is 200 π cm3. By formula, l2 = r2 + h2 ⇒ l2 = 52 + 122 ⇒ l2 = 25 + 144 ⇒ l2 = 169 ⇒ l = = 13 cm Total surface area of remaining solid = Curved surface area of cylinder + curved surface area of cone + base area of cylinder = 2πRH + πrl + πR2 = π(2RH + rl + R2) = π(2 × 5 × 12 + 5 × 13 + 52) = π(120 + 65 + 25) = 210 π cm2. Hence, the volume of the remaining solid is 200 π cm3 and total surface area of remaining solid is 210 π cm2.

Mathematics

From a circular cylinder of diameter 10 cm and height 12 cm, a conical cavity of the same base radius and of the same height is hollowed out. Find the volume and the whole surface of the remaining solid. Leave the answer in π

Mensuration

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