Question

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

Answer 1

Given :-

Each side of the cube = 7 cm

Radius = 7/2 cm

To Find :-

The surface area (TSA) of the solid.

Analysis :-

The total surface area of solid (TSA) = Surface area of cubical block + CSA of hemisphere – Area of base of hemisphere

Solution :-

We know that,

• TSA = Total surface area
• CSA = Curved surface area
• r = Radius
• d = Diameter

Given that,

Each side of cube is 7 cm. So, the radius will be 7/2 cm.

TSA = CSA + Area of base of hemisphere

Substituting these data, we get

∴ TSA of solid = $\sf 6 \times (side)^{2}+2 \pi r^{2}- \pi r^{2}$

Taking value of pi as 22/7 and substituting the given values,

$\implies \sf 6 \times (7)^{2}+\dfrac{22}{7} \times \dfrac{7}{2} \times \dfrac{7}{2}$

$\implies \sf (6 \times 49)+\bigg(\dfrac{77}{2} \bigg)$

$\implies \sf 294+38.5$

$\implies \sf 332.5\: cm^{2}$

Therefore, the surface area of the solid is 332.5 cm²

To Note :-

If a solid is molded by two or more than two solids then we need to divide it in separate solids to calculate its surface area.

TSA = CSA + Area of base of hemisphere

Answer 2

It is given that each side of cube is 7 cm. So, the radius will be 7/2 cm.

We know,

The total surface area of solid (TSA) = surface area of cubical block + CSA of hemisphere – Area of base of hemisphere

∴ TSA of solid = 6×(side)2+2πr2-πr2

= 6×(side)2+πr2

= 6×(7)2+(22/7)×(7/2)×(7/2)

= (6×49)+(77/2)

= 294+38.5 = 332.5 cm2

So, the surface area of the solid is 332.5 cm2