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In figure, from a cuboidal solid metallic block of dimensions $15 cm × 10 cm × 5 cm,$ a cylindrical hole of diameter $7 cm$ is drilled out. Find the surface area of the remaining block. $Use π = 227$

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291 cm 2

193 cm 2

283 cm 2

583 cm 2

answer is D.

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Detailed Solution

It is given that the length, breadth and height of the cuboidal solid metallic block are

l = 15 cm

b = 10 cm

and

h = 5 cm

The volume of a cube is expressed as,

V = l b h

where l, b and h be the length, width and height of a cube.
The diameter of the cylindrical hole is,

D = 7

cm, so the radius will be,
Question Image

Thus, the surface area of remaining block is,

A s = surface area of cuboid+curved surface area of cylinder-2 area of base

⇒ A s = 2 l b + b h + l h + 2 π r h − 2 π r 2

Thus, the surface area of the remaining block is

583 c m 2

.
Therefore, option (4) is correct.

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