Question

a cubical block of side 7 cm is surmounted by a hemisphere what is the greatest diameter of the hemisphere can have find the surface area of the solid

Answer 1

Greatest diameter of hemisphere =side of cube =7 cm
surface area of solid =Area of cube +curved surface area of hemisphere-base area of hemisphere
=294+77-77/2
=294+77-38.5
=371-38.5
=332.5
Hence,surface area of solid cube =332.5

Answer 2

Solution:

Given:

=> Edge of cube = 7 cm.

=> Diameter of hemisphere = 7 cm.

=> Radius of hemisphere = 7/2 cm.

To Find:

=> Surface area of solid.

Formula used:

$\sf{\implies Area\;of\;cube=6a^{2}}$

$\sf{CSA\;of\;hemisphere=2\pi r^{2}}$

$\sf{Area\;of\;circle=\pi r^{2}}$

So,

Area of cube = 6a²

=> 6 × 49

=> 294 cm²

CSA of hemisphere = 2πr²

$\sf{\implies 2\times \dfrac{22}{7}\times \dfrac{7}{2}\times \dfrac{7}{2}}$

$\sf{\implies \dfrac{154}{2}}$

=> 77 cm²

Area of circle = πr²

$\sf{\implies \dfrac{22}{7}\times \dfrac{7}{2} \times \dfrac{7}{2}}$

$\sf{\implies 38.5\;cm^{2}}$

Total area = Area of cube + CSA of hemisphere - Base area of hemisphere

=> 294 + 77 - 38.5

=> 332.5 cm²