Question

A hemispherical depression is cut out from one face of a cubical block of side 7 cm, such that the diameter of the hemisphere is equal to the edge of the cube. Find the surface area of remaining solid.

Answer 1

Given:

Diameter of hemisphere = Edge of cube = $7cm$

Therefore, radius of the hemisphere = $\frac{7}{2}$ cm.

The total surface area of solid = Area of 5 sides of cube + CSA of Hemisphere + Face area remaining after the hemispherical part is removed.

Area of 5 sides of the cube is 5a²
= $5\times 7^2$
= $245cm²$

CSA of hemisphere <dictate and write: CSA = $2\pi r^2$

= $2\times \frac{22}{7}\times \frac{7}{2}\times \frac{7}{2}$
= $77cm²$

Area after removing the hemispherical part
= $7²-\pi r^2$
= $7²-\frac{22}{7}\times (\frac{7}{2}{)}^2$

= $49-38.5$
= $10.5cm²$

Surface area of the solid
= $245cm²+77cm²+10.5cm²$

= $332.5cm²$