Question

There is a solid wooden cuboidal block of length, breadth and height 10 m, 8 m and 5 m respectively. On the top face of the block is a hemispherical depression of radius 3 m. What is the surface area of the solid so obtained?

• A. 301
• B. 408
• C. 348
• D. 368

Answer 1

The correct option is D

368

The Total surface area of the wooden object consists of the following-

5 faces of the cuboid

Entire surface of the $6^{t}h$ face except the region marked in yellow (region scooped out)

Hemisphere formed after scooping out wood

The 5 faces will include all faces except top face which has length and breadth-

Area of 5 faces = 10 × 8 + 5 × 8 + 5 × 8 + 10 × 5 + 10 × 5

= 260 $c{m}^2$

Area of entire surface except yellow circular region

= 10 × 8 - $\pi$$(3{)}^2$

= 51.7 $c{m}^2$

Area of hemisphere = 2$\pi$$(3{)}^2$

= 56.5 $c{m}^2$

Total surface area = 260 + 51.7 +56.5

= 368.2 $c{m}^2$