Question

A dome of a building is in the form of a hemisphere. From inside, it was white-washed at the cost of ₹498.96. If the cost of white-washing is ₹2.00 per square metre, find the radius of dome​

Answer 1

Answer:

Let, r m be the inner radius of the hemispherical dome. Then

(i) Inside surface area of the hemispherical dome = Total cost/Cost per square metre

= 498.96/2 m2 = 249.48 m2

Now, 2πr2 = 249.48

⇒ r2 = 249.48 x 7/2 x 22 = 39.69 ⇒ r = root under(√39.69) = 6.3 m

(ii) Volume of the air inside the dome

= Volume of the hemispherical dome

= 2/3πr3 = 2/3 x 22/7 x (6.3)3 m3 = 523.908 m3

Answer 2

$\leqslant \geqslant \leqslant \geqslant \leqslant \geqslant \leqslant \geqslant \leqslant \geqslant \leqslant \geqslant \leqslant \geqslant \leqslant \geqslant \leqslant \geqslant \leqslant \geqslant \leqslant \geqslant \leqslant \geqslant \leqslant$

Cost of white washing dome = Rs.498.96

Cost of white washing 1m² area = Rs.2

$\sf \: CSA= \frac{498.96}{2} = 249.48 \: {m}^{2}$

Let, radius = r ,CSA =249.48 m²

$\sf \: CSA= 2\pi {r}^{2}$

$\sf \:249.48= 2 \times 3.14 \times {r}^{2}$

$\sf {r}^{2} = 37.9 \: {m}^{2}$

$\sf \: r = 6.3 \: m$