Question

A cube of side 7 cm is surmounted by a hemisphere.Find the largest possible diameter of the hemisphere.

Answer 1

The hemisphere can occupy whole of the surface of cube ..
Hence,
largest diameter of hemisphere =side of cube
=7cm
base of hemisphere falls on cube so , that area should no from part of solid..
surface area of solid=area of cube+csa of hemisphere-base area of hemisphere
Area of cube,
side=7
area of cube=6a^2
=6(7)^2

=6×7×7
=6×49
=294cm^2
CSA of hemisphere,
diameter 7cm
Radius =3.5
CSA=2pie r^2
2×22/7×3.5×3.5
=77cm^2
base area of hemisphere,
Radius=7/2
3.5
base of area =pie r^2
=22/7×3.5×3.5
=38.5
surface area of solid =area of cube+CSA of hemisphere-base area of hemisphere
=294+77-38.5
=371-38.5
=332.5cm^2