In the given figure, from a cuboidal solid metalic 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. (Take $π = \frac{22}{7}$ ). [CBSE 2015]

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Solution

Surface area of the remaining block
= Total Surface area of cubic block + Curved Surface area of cylinder − 2(Area of circular base)
$= 2 (l b + b h + l h) + 2 π r h - 2 π r^{2} = 2 (15 \times 10 + 10 \times 5 + 15 \times 5) + 2 \times \frac{22}{7} \times \frac{7}{2} \times 5 - 2 \times \frac{22}{7} \times {(\frac{7}{2})}^{2} = 2 \times 275 + 110 - 77 = 583 {cm}^{2}$

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In the given figure, from a cuboidal solid metalic 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. (Take π=227). [CBSE 2015]

Surface area of the remaining block = Total Surface area of cubic block + Curved Surface area of cylinder − 2(Area of circular base) =2(lb+bh+lh)+2πrh−2πr2=2(15×10+10×5+15×5)+2×227×72×5−2×227×(72)2=2×275+110−77=583 cm2

In the given figure, from a cuboidal solid metalic 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. (Take $π = \frac{22}{7}$ ). [CBSE 2015]