Question

A cuboidal block of side $7cm$ is surmounted by a hemisphere. What is the greatest diameter of the hemisphere can have also find the total surface area of the solid.

Answer 1

We have

side of cuboidal block= 7 cm

Clearly greatest diameter of the hemisphere is equal to the length of an edge of the cube is $7cm$

Radius of hemisphere $=\frac{7}{2}cm$

Now, Total surface area of the solid

$=$ surface area of the cube + curved surface area of the hemisphere - Area of the base of the hemisphere.

$=(6\times (edge{)}^2-\pi r^2+2\pi r^2){cm}^2$

$=\{6\times 7^2+2\times \frac{22}{7}\times {\left(\frac{7}{2}\right)}^2-\frac{22}{7}\times {\left(\frac{7}{2}\right)}^2\}{cm}^2$

$=332.5{cm}^2$