Q1. [4] § 12.3 Volume of a Combination of Solids § 12.4 Summary
The word 'circus' has the same root as 'circle'. In a closed circular area, various entertainment acts including human skill and animal training are presented before the crowd.
A circus tent is cylindrical upto a height of 8 m and conical above it. The diameter of the base is 28 m and total height of tent is 18.5 m.
The word 'circus' has the same root as 'circle'. In a closed circular area, various entertainment acts including human skill and animal training are presented before the crowd. A circus tent is cylindrical upto a height of 8 m and conical above it. The diameter of the base is 28 m and total height of tent is 18.5 m. Based on the above, answer the following questions:
- (i) Find slant height of the conical part. [1]
- (ii) Determine the floor area of the tent. [1]
- (iii) Find area of the cloth used for making tent. OR Find total volume of air inside an empty tent. [2]
Previously asked in CBSE board exam
2024 30/2/1 Q37
Generated by claude-sonnet-4-6 · 2026-06-15 10:33 · grounding stimulus
Model Answer
Given: Diameter = 28 m → Radius (r) = 14 m, Height of cylinder (h₁) = 8 m, Total height = 18.5 m → Height of cone (h₂) = 18.5 − 8 = 10.5 m
(i) Slant height of conical part:
$$l = \sqrt{r^2 + h_2^2} = \sqrt{14^2 + 10.5^2} = \sqrt{196 + 110.25} = \sqrt{306.25} = 17.5 \text{ m}$$
(ii) Floor area of tent:
$$= \pi r^2 = \frac{22}{7} \times 14 \times 14 = 616 \text{ m}^2$$
(iii) Area of cloth used (CSA of cylinder + CSA of cone):
$$= 2\pi r h_1 + \pi r l = \pi r(2h_1 + l) = \frac{22}{7} \times 14 \times (16 + 17.5) = 44 \times 33.5 = \mathbf{1474 \text{ m}^2}$$
OR Total volume of air:
$$= \pi r^2 h_1 + \frac{1}{3}\pi r^2 h_2 = \pi r^2\!\left(h_1 + \frac{h_2}{3}\right) = \frac{22}{7} \times 196 \times \left(8 + 3.5\right) = 616 \times 11.5 = \mathbf{7084 \text{ m}^3}$$
Source: Mensuration (Cylinders and Cones), Class 10 Mathematics
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Explanation
- Slant height uses Pythagoras: $l = \sqrt{r^2 + h_{cone}^2}$. Remember to find cone's height separately (Total − Cylinder height).
- Floor area is just the base circle (πr²) — not curved surface.
- For cloth area, only curved surfaces are counted (no base); combine CSA of cylinder and cone.
- For volume, add volume of cylinder + volume of cone. Factorising πr² saves calculation time and reduces errors.
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