Real life Problems related to different Solid Objects
Multiple Choice Questions (MCQ)
1. What is the volume of a cylinder with radius 3 cm and height 7 cm?
A. 63π cm³
B. 21π cm³
C. 27π cm³
D. 198π cm³
Answer: A. 63π cm³
2 The total surface area of a cone with radius 4 cm and slant height 5 cm is:
A. 20π cm²
B. 36π cm²
C. 72π cm²
D. 56π cm²
Answer: D. 56π cm²
3. Which of the following solids has the formula 43πr3 for volume?
A. Cylinder
B. Cone
C. Sphere
D. Hemisphere
Answer: C. Sphere
4. A composite solid consists of a hemisphere (radius = 3 cm) attached to a cylinder of the same radius and height 6 cm. What is the total volume (in terms of π)?
A. 81π cm³
B. 117π cm³
C. 54π cm³
D. 90π cm³
Answer: D. 90π cm³
5. Which of the following best represents a real-life use of surface area of a cone?
A. Measuring how much water a tank can hold
B. Calculating the weight of a metal sphere
C. Finding the cloth reuired to cover a conical tent
D. Estimating the cost of a wooden cube
Answer: C. Finding the cloth reuired to cover a conical tent
Short Answer Questions (SAQ)
1.Write the formula for the total surface area of a cylinder.
Answer: TSA = 2πr(h+r)
2. A sphere has radius 2 cm. Find its volume in terms of π.
Answer: V = 43πr3 = 43π × 8 = 322π cm³
3. A cone has radius 1.5 m and slant height 2 m. Find its lateral surface area.
Answer: Lateral surface area πrl = π × 1.5 × 2 = 3π m²
Long Answer Questions (LAQ)
1. A water tank is in the shape of a cylinder with radius 2 m and height 3.5 m.
a) Calculate the volume of water it can hold.
b) How many litres of water can it store? (1 m³ = 1000 litres)
Answer: a) Volume = π × r² × h = π × 2² × 3.5 = 14π m³
b) Volume in litres = 14π × 1000 ≈ 43982.3 litres
2. A toy consists of a cone mounted on a hemisphere. The radius of both is 3 cm and the height of the cone is 4 cm.
a) Find the volume of the toy.
b) If the toy is made of plastic that costs ₹0.10 per cm³, find the cost of one toy.
Answer: a) Volume of cone = 13πr2h = 13π × 9 × 4 = 12πcm³
Volume of hemisphere = 12 × 43πr3 = 12 × 43π × 27 = 18π cm³
Total = 12π + 18π = 30π ≈ 94.25 cm³
b) Cost = 94.25 × 0.10 = ₹9.43