Question

The total height of the toy is 15.5
4. 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

Answer:

The total height of the toy is 15.5

4. 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.

Step-by-step explanation:

The total height of the toy is 15.5

4. 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.

The total height of the toy is 15.5

4. 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.The total height of the toy is 15.5

4. 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.The total height of the toy is 15.5

4. 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.The total height of the toy is 15.5

4. 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 2

Given:

• A cubical block of 7cm is surmounted by a hemisphere.

Find:

• Greatest diameter the hemisphere can have.
• Surface Area of Solid.

Solution:

Hemisphere, can occupy whole side of cube.

$\therefore$ Greatest Diameter of Hemisphere = Side of Cube = 7cm

Now,

$\footnotesize{\boxed{\red{\rm Surface \: area \: of \: solid = area \: of \: cube + c.s.a \: of \: hemisphere - base \: area \: of \: hemisphere}}}$

Here,

$\rm \dashrightarrow Area \: of \: cube = 6 {(side)}^{2}$

where,

• Side = 7cm

So,

$\pink{\rm \dashrightarrow Area \: of \: cube = 6 {(side)}^{2} }$

$\pink{\rm \dashrightarrow Area \: of \: cube = 6 {(7)}^{2} }$

$\pink{\rm \dashrightarrow Area \: of \: cube = 6 \times 49}$

$\pink{\rm \dashrightarrow Area \: of \: cube = 294 {cm}^{2} }$

$\rm \therefore Area \: of \: cube = 294 {cm}^{2}$

_________________________

⧴ Diameter of Hemisphere = 7cm

⧴ Radius of Hemisphere = 7/2 = 3.5cm

Now,

$\rm \dashrightarrow C.S.A \: of \: hemisphere = 2 \pi {r}^{2}$

where,

• Radius, r = 3.5cm
• π = 22/7

So,

$\purple{\rm \dashrightarrow C.S.A \: of \: hemisphere = 2 \pi {r}^{2} }$

$\purple{\rm \dashrightarrow C.S.A \: of \: hemisphere = 2 \times \dfrac{22}{7} \times {(3.5)}^{2} }$

$\purple{\rm \dashrightarrow C.S.A \: of \: hemisphere =\dfrac{44}{7} \times 12.25}$

$\purple{\rm \dashrightarrow C.S.A \: of \: hemisphere =\dfrac{539}{7}}$

$\purple{\rm \dashrightarrow C.S.A\: of \: hemisphere =77 {cm}^{2} }$

$\rm \therefore C.S.A\: of \: hemisphere = 77 {cm}^{2}$

_________________________

Now,

$\rm \dashrightarrow Base \: area \: of \: hemisphere = \pi {r}^{2}$

where,

• π = 22/7
• r = 3.5cm

So,

$\orange{\rm \dashrightarrow Base \: area \: of \: hemisphere = \pi {r}^{2} }$

$\orange{\rm \dashrightarrow Base \: area \: of \: hemisphere = \dfrac{22}{7} \times {(3.5)}^{2} }$

$\orange{\rm \dashrightarrow Base \: area \: of \: hemisphere = \dfrac{22}{7} \times 12.25}$

$\orange{\rm \dashrightarrow Base \: area \: of \: hemisphere = \dfrac{269.5}{7}}$

$\orange{\rm \dashrightarrow Base \: area \: of \: hemisphere = 38.5 {cm}^{2} }$

$\rm \therefore Base \: area \: of \: hemisphere = 38.5 {cm}^{2}$

_________________________

Now,

$: \to \footnotesize{\red{\rm Surface \: area \: of \: solid = area \: of \: cube + c.s.a \: of \: hemisphere - base \: area \: of \: hemisphere}}$

where,

• Area of Cube = 294cm²
• C.S.A. of Hemisphere = 77cm²
• Base area of Hemisphere = 38.5cm²

So,

$: \to \footnotesize{\green{\rm Surface \: area \: of \: solid = area \: of \: cube + c.s.a \: of \: hemisphere - base \: area \: of \: hemisphere}}$

$: \to \green{\rm Surface \: area \: of \: solid = 294+ 77 - 38.5}$

$: \to \green{\rm Surface \: area \: of \: solid = 371 - 38.5}$

$: \to \green{\rm Surface \: area \: of \: solid = 332.5 {cm}^{2} }$

_________________________

Hence, the greatest diameter Hemisphere can have is 7cm

Surface Area of Solid is 332.5cm²