Question

A hemispherical dome of building needs to be painted. If the radius of the dome is 2.8m find the cost of painting it, given that the cost of painting per m2 is Rs.400

Answer 1

GIVEN :-

• Radius of the hemispherical dome = 2.8 m

• Cost of painting per m² = Rs 400

TO FIND :-

• Cost of painting the hemispherical dome.

SOLUTION :-

Round surface of the dome is to be painted.

So we should find the curved surface area of the hemisphere .

Formula to find the curved surface area of the hemisphere  $\bf = 2\pi r^2$

$\longrightarrow 2\times \dfrac{22}{7} \times 2.8 \times 2. 8 \\\\\longrightarrow 2\times 22 \times 0.4 \times 2.8 \\\\\longrightarrow 49.28$

Curved surface area of the hemispherical dome = 49.28 m²

 Cost of painting 1 m² = Rs 400

∴ Cost of painting 49.28 m² = 400 × 49.28

                                              = Rs 19712

Answer 2

✨GIVEN:

• Radius of hemispherical dome = 2.8m
• Rate of painting = rs. 400/m²

✨FIND:

• Cost of painting the dome = ?

✨SOLUTION:

we know,

Area to be painted = Area of hemisphere

so, Area of hemisphere = 2 π r²

where,

• r = 2.8m
• π = $\bold{\frac{22}{7}}$

putting these values in the area if hemisphere we got

$\bold{ \to Area \: of \: hemisphere =2 \times \frac{22}{7} \times {(2.8)}^{2} }$

$\bold{ \implies 2 \times \frac{22}{7} \times 7.84 }$

$\bold{ \implies 2 \times \frac{22}{ \cancel7} \times \cancel{ 7.84 }}$

$\bold{ \implies 2 \times 22 \times 1.12}$

$\bold{ \implies 44\times 1.12}$

$\bold{ \implies 49.28 {m}^{2} }$

Hence, Area of hemisphere = 49.28m²

Now,

Cost of painting 1m² = rs.400

So, cost of painting 49.28m² = 400 × 49.28

= rs. 19712

Hence, cost of painting dome is rs. 19712