Question

[BASIC/STANDARD]
28. A circus tent is in the form of a right circular cylinder and a right circular cone above
it. The diameter and the height of the cylindrical portion of the tent are 98 m and 5 m
respectively
. If the total height of the tent is 20 m, find the volume of air in the tent.
[Basic/STANDARD​

Answer 1

Given :-

• Height of cylindrical part(h)= 5m
• Diameter of cylindrical part (d)= 98
• or Radius(r)= 98/2= 49m

• Height of conical part (H)= 20-5= 15cm
• Radius of cone = Radius of cylinder= 49m

To find :-

we have to find the volume of air present in the tent

Solution:-

Volume of air= Volume of cone+volume of cylinder

$\bullet\sf\ Volume\ of\ cylinder= \pi r^2 h\\ \\ \bullet\sf\ Volume\ of\ cone= \dfrac{1}{3}\pi r^2 h$

$\sf\ V.\ of\ air= \dfrac{1}{3}\pi r^2 H+\pi r^2h\\ \\ \\ \implies\sf\ \ V.\ of\ air= \dfrac{1}{3}\pi r^2\big(H+3h\big)\\ \\ \\ \implies\sf\ V.\ of\ air= \dfrac{1}{3}\times \dfrac{22}{7}\times 49\times 49\big(20+3\times 5)\\ \\ \\ \implies\sf\ V.\ of\ air= \dfrac{22\times 49\times 49\times 35}{3\times 7}\\ \\ \\ \implies\sf\ V.\ of\ air= \cancel{\dfrac{1848770}{21}}\\ \\ \\ \implies\boxed{\sf\purple{ Volume\ of\ air = 88036.67m^3}}$

Answer 2

Answer:

Given :-

Height of cylindrical part(h) = 5m

Diameter of cylindrical part (d) = 98

Height of conical part (H) = 20 - 5 = 15m

Radius of cone = Radius of cylinder = 49m

To Find :-

volume of air present in the tent

SoluTion :-

We know that

Volume of cylinder

$\sf \large\bold\pi \ {r}^{2} h$

Volume of cone

$\large \sf \: \dfrac{1}{3} \pi {r}^{2} h$

Radius = D/2

Radius = 98/2

Radius = 49 m

Volume of air = Volume of cone + volume of cylinder

Now,

Volume of air = ⅓πr²(H + 3h)

=> ⅓ × 22/7 × 49 × 49 (20 + 3 × 5)

=> ⅓ × 22/7 × 49 × 49 (20 + 15)

=> ⅓ × 22/7 × 49 × 49 (35)

=> ⅓ × 22 × 7 × 49 × 35

=> 22 × 7 × 49 × 35/3

=> 154 × 1715/3

=> 264110/3

=> 88,036