Question

A cubical block of side 7cm is surmounted by a hemisphere of the largest size. Find the surface area of the resultant solid.

Answer 1

The largest sphere surmounted on the hemisphere would have the diameter equal to the edge of the cube. While finding the total surface area the base of the hemisphere and the face of the cube surmounting the hemisphere will not be considered.

Complete step-by-step answer:

The resulting solid will look like:

Edge of cube: 7cms
Radius of the largest hemisphere: 3.5
Curved surface area of cube: $2\pi {r^2}$
Total Surface area of cube: $6{a^2}$
Since one surface is hidden, so now the area is: $5{a^2}$
Resultant area of solid: $2\pi {r^2} + 5{a^2}$
Taking $\pi = 3.14$
$
  2\pi \times (3.5 \times 3.5) + 5 \times 7 \times 7 \\
  321.93{\text{ c}}{{\text{m}}^2} \\
$

Note: In these types of questions, the figure should be made correctly and the surface which must be involved in the surface area should be checked, Also it is important to remember all the respective formulas of the mensuration.