Mathematics
From a solid cylinder whose height is 16 cm and radius is 12 cm, a conical cavity of height 8 cm and of base radius 6 cm is hollowed out. Find the volume and total surface area of the remaining solid.
Mensuration
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Answer
Given,
Height of the cylinder (H) = 16 cm
Radius of the base of cylinder (R) = 12 cm
Height of the cone (h) = 8 cm
Radius of the base of cone (r) = 6 cm
![From a solid cylinder whose height is 16 cm and radius is 12 cm, a conical cavity of height 8 cm and of base radius 6 cm is hollowed out. Find the volume and total surface area of the remaining solid. Cylinder, Cone, Sphere, Concise Mathematics Solutions ICSE Class 10.](https://cdn1.knowledgeboat.com/img/cm10/q2-c20-ex-20-f-cylinder-cone-sphere-concise-maths-solutions-icse-class-10-301x343.png)
(i) Volume of remaining part (V) = Volume of cylinder - Volume of cone
Hence, volume of remaining part = 6939.43 cm3.
(ii) By formula,
⇒ l2 = r2 + h2
⇒ l2 = 62 + 82
⇒ l2 = 36 + 64
⇒ l2 = 100
⇒ l2 = 102
⇒ l = 10 cm.
Thus,
Total surface area of remaining solid (T) = Curved surface area of cylinder + Curved surface area of cone + Base area of cylinder + Area of circular ring on upper side of cylinder
(T) = 2πRH + πrl + πR2 + π(R2 - r2)
Hence, total surface area of remaining solid = 2187.43 cm2.
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