Question

A cubical block of side 7 cm is surmounted by a hemisphere. What is the greatest
diameter the hemisphere can have? Find the volume of the solid.​

Answer 1

The hemishphere can occupy the side of the cube .

so the greatest diameter of hemisphere is side of the cube =7cm.

surface area of solid =area of cube +curved surface area of hemisphere -base area of hemisphere (as base of hemisphere falls on cube so its must not be included)

=6a²+2×(Pi)×r²-(Pi)×r²

=(6×7²)+(2×22/7×7/2×7/-(22/7×7/2×7)

=294cm²+77cm²-77/2cm²

=(294+77-38.5)cm²

=(371-38.5)cm²

=332.5cm²

Hence the surface area of solid is 332.5cm².