Question

A dome of a building is in the form of hemisphere. From inside, it was white washed at the cost of Rs 498.96. If the cost of white washing is Rs 2.00 per square metre, find the volume of air inside the dome
plz telll fast as fast a possible

Answer 1

Answer

• Volume of the air inside the dome is 277.93 m³

Explanation

Given

• For white washing the dome from the inside it costs 498.06
• It costs ₹ 2.00 per m²

To Find

• Volume of the air inside the dome

Solution

• First find the area of the dome, then using that find the radius 9f the hemisphere and with that on simple substitution gets us our volume!!

✭ Area of the dome

→ Area = Total Cost/Cost per m²

→ Area = 498.96/2

→ Area = 249.48 m²

✭ Radius of the hemisphere

→ TSA = 3πr²

→ 249.48/3 = πr²

→ 83.16 × 7/22 = r²

→ 582.12/22 = r²

→ 26.46 = r²

→ √26.46 = r

→ Radius = 5.1 m

✭ Volume of the hemisphere

→ Volume = ⅔πr³

→ Volume = ⅔ × 22/7 × 5.1³

→ Volume = 277.93 m³

Answer 2

ɢɪᴠᴇɴ :-

$\dashrightarrow$It was white washed at cost of = ₹498.96

$\dashrightarrow$Cost of white washing = ₹2.00

ᴛᴏ ғɪɴᴅ :-

The volume of air inside the dome.

Sᴏʟᴜᴛɪᴏɴ :-

Volume of air inside dome = Volume of hemisphere

= $\frac{2}{3}\pi {r}^{3}$

Let the radius of dome be 'r' m

Surface area of dome = $249.48^2$

$2\pi{r}^{2} = 249.48$

$2\times\frac{22}{7}\times{r}^{2} =249.48$

${r}^{2} = 39.69$

$r = \sqrt{39.69}$

r = 6.3m

Volume of air inside dome = Volume of hemisphere

= $\frac{2}{3}\pi {r}^{3}$

= $\frac{2}{3}\times\frac{22}{7}\times{6.3}^{3}$

$\pink{ ⋆ }$$\bold\red{523.9m^3}$