Question

a hemispherical dome of a building needs to be painted . if the circumference of the base of the dome is 17.6,find the cost of painting it ,given the cost of painting is RS 5per 100 cm

Answer 1

Circumference = 2πr
2πr = 17.6
r = 17.6*7/22*2
r = 2.8cm.

Surface area = 2πr²
= 2*3.14*2.8*2.8
= 49.23cm²

100cm² costs ₹5
1cm² costs 5/100
49.23cm² costs 5/100*49.23 = ₹2.46

Answer 2

Cᴏʀʀᴇᴄᴛ Qᴜᴇsᴛɪᴏɴ :-

• A hemispherical dome of a building needs to be painted . if the circumference of the base of the dome is 17.6 m. Find the cost of painting it ,given the cost of painting is Rs. 5 per 100 cm².

Gɪᴠᴇɴ :-

• Circumference of the base of the dome is 17.6 m.

• Cost of painting is Rs.5 per 100 cm.

Tᴏ Fɪɴᴅ :-

• Circumference of the dome.

• Curve surfaced area of the dome.

• Cost of painting the dome.

Sᴏʟᴜᴛɪᴏɴ :-

• Let the radius of dome be r.

${\boxed{{\bf{Circumference \: of \: dome \: = Circumference \: of \: circle \: with \: radius \: r.}}}}$

$\sf\large\blue{⇝17.6 = 2\pi r}$

$\sf\large\blue{⇝17.6 = 2 \times \frac{22}{7} \times r}$

$\sf\large\blue{⇝17.6 \times \frac{7}{2 \times 22} = r}$

$\sf\large\blue{⇝r = 17.6 \times \frac{7}{2 \times 22} \: m }$

$\sf\large\blue{⇝r = 2 .8 \: m}$

$\sf\large\blue{⇝r = 2 .8 \times 100 \: cm}$

$\sf\large\blue{⇝r = 280 \: cm}$

• $\sf\large{The \: curved \: surface \: area \: of \: the \: dome = 2\pi r}$

$\sf\large\purple{⇝2 \times \frac{22}{7} \times (280) \times (280) {cm}^{2} }$

$\sf\large\purple{⇝2 \times 22 \times (40)\times (280) {cm}^{2} }$

$\sf\large\purple{⇝492800 \: cm ^{2} }$

• Now, Cost of painting 100 cm² = Rs.5

$\sf\large \pink{ ⟶ Cost \: of \: painting \: 1 \: cm ^{2} = Rs \: 5 \times \frac{1}{100} }$

$\sf\large \pink{ ⟶ Cost \: of \: painting \: 492800\: cm ^{2} = rs \: 5 \times \frac{1}{100} \times 492800 }$

$\sf\large \pink{⟶ Cost \: of \: painting \: 492800\: cm ^{2} = Rs. \: 24640}$

${\boxed{{\bf{∴Cost \: of \: painting \: the \: dome = Rs.24640.}}}}$