In the given figure from a cuboidal solid metallic block of dimensions `15 cm xx 10 cm xx 5 cm ` a cylindrical hole of diamter 7 cm is drilled out . Find the suface area of the remaining block .

Options

A. `450 cm^2 `
B. `553 cm^2 `
C. `550 cm^2 `
D. `583 cm^2 `

Answer

D

Explanation

Length of the cuboid l= 15 cm
Breadith of the cuboid b b= 10 cm
Height of the cuboid ,h = 5 cm
Radius of the cylinder ,r = 7/2 cm
Height of the cylinder h= 5 cm
Surface area of the remaining block
= total surface area of the cuboid - area of two circular faces of the cylinder + curved surface area of the cylinder
`=2(lb+ bh +lh )-2 xx pi r^2 + 2 pi rh `
`=[2(15 xx 10+10xx 5 + 15 xx5)-2xx 22/7xx7/2xx7/2xx7/2+2 xx22/7 xx7/2xx5] cm^2`
`=(550-77 +110 )cm^2 = 583 cm^2 `
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