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Home » 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.
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.
Class 10 | Cylinder, Cone and Sphere (Surface Area and Volume) | Exercise 20F | ICSE | Selina
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.

Selina Solutions Concise Class 10 Maths Chapter 20 ex. 20(F) - 1

Radius of solid cylinder (R) = 12 cm

And, Height (H) = 16 cm

    \[\begin{array}{*{35}{l}} Volume\text{ }=\text{ }\pi {{R}^{2~}}h\text{ }=\text{ }22/7\text{ }x\text{ }12\text{ }x\text{ }12\text{ }x\text{ }16 \\ =\text{ }50688/7\text{ }c{{m}^{3}} \\ Radius\text{ }of\text{ }cone\text{ }\left( r \right)\text{ }=\text{ }6\text{ }cm,\text{ }and\text{ }height\text{ }\left( h \right)\text{ }=\text{ }8\text{ }cm. \\ Volume\text{ }=\text{ }1/3\text{ }\pi {{r}^{2~}}h \\ =\text{ }1/3\text{ x }22/7\text{ x }6\text{ x }6\text{ x }8 \\ =\text{ }2112/7\text{ }c{{m}^{3}} \\ \end{array}\]

(i) Volume of remaining solid = 50688/7 – 2112/7

= 48567/7

= 6939.43 cm3

(ii) Slant height of cone l = (h2 + r2)1/2

= (62 + 82)1/2 = (36 + 64)1/2 = (100)1/2 = 10 cm

Thus,

Total surface area of remaining solid = curved surface area of cylinder + curved surface area of cone + base area of cylinder + area of circular ring on upper side of cylinder

Selina Solutions Concise Class 10 Maths Chapter 20 ex. 20(F) - 2

= 15312/7

= 2187.43 cm2

i

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