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From a solid cylinder whose height is $8 cm$ and radius $6 cm,$ a conical cavity of height $8 cm$ and of base radius $6 cm$ , is hollowed out. Find the volume of the remaining solid correct to two places of decimal. Also find the total surface area of the remaining solid.

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602.88 cm 3

and

603.42 cm 2

652.88 cm 3

and

600.42 cm 2

482.88 cm 3

and

503.42 cm 2

872.88 cm 3

and

613.42 cm 2

answer is A.

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Detailed Solution

It is given that, the radius and height of the cylinder is

and h=8cm.
Also, the radius and height of the cone is given as,

and

h = 8 cm

.
The volume of a circular cone is expressed as,

V = 13 π r 2 h

, where

r

be the radius of a circular cone.
The volume of the cylinder is,
Question Image

So, the volume of the cone is,
Question Image

Thus, the resulting volume of the solid is,
Question Image

The slant length of the cone is,
Question Image

The total surface area of final solid is,

A = π r l + 2 π r h + π r 2 ⇒ π 610 + 2 π 68 + π 62 ⇒ 188 + 301.44 + 113.04 ⇒ 603.42 cm 2

Thus, the resulting volume of the solid and total surface area of final solid is

602.88 cm 3

and

603.42 cm 2

respectively.
Therefore, option (1) is correct.

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