Question

A cubical block of side 7 cm is surmounted by a hemisphere of diameter equal to the side of the cube.Find the surface area of the solid.

• A. $332.5c{m}^2$
• B. $322.5c{m}^2$
• C. $342.5c{m}^2$
  
• D. $38.5c{m}^2$
  

Answer 1

Answer: (A)

$332.5c{m}^2$

The greatest diameter=side of the cube=$7$cm.

The radius of the hemisphere =$3.5$cm.

Now,

The Surface Area of Solid=Surface Area of Cube - Surface Area of Base Hemisphere + Curve Surface Area of Hemisphere

Surface Area of Cube

=$6\times sid{e}^2$

=$6\times 7\times 7$

=$294$sq cm

Surface Area of Base of Hemisphere is,

=$\pi r^2$

=$\frac{22}{7}\times {3.5}^2$

=$38.5c{m}^2$

Curved Surface Area of Hemisphere is,

=$2\times 38.5$

=$77$sq cm

$\therefore$ total Surface Area is $=294-38.5+77$

$=332.5$sq cm.