The curved surface area of a cylinder is 2πrh and the volume of a sphere is (4/3)πr³, so this Class 9 sheet opens with the two curved-surface formulas. The answers add a cube's 6a² surface area and a cone's (1/3)πr²h volume.
Key Takeaways
The curved surface area of a cylinder is 2πrh (Q1).
The volume of a sphere is (4/3)πr³ (Q2).
Q3 records 6a² as the surface area of a cube.
Section A: Multiple Choice Questions (1 Mark Each)
Choose the correct option for each question.
1.The curved surface area of a cylinder of radius r and height h is
(a) 2πr(r + h)(b) 2πrh(c) πr²h(d) 2πr²
2.The volume of a sphere of radius r is
(a) (4/3)πr³(b) πr³(c) (1/3)πr³(d) 4πr²
3.The total surface area of a cube of edge a is
(a) a³(b) 6a²(c) 4a²(d) 2a²
4.The volume of a cone of radius r and height h is
(a) πr²h(b) (2/3)πr²h(c) (1/3)πr²h(d) (4/3)πr³
5.The total surface area of a hemisphere of radius r is
(a) 2πr²(b) 3πr²(c) 4πr²(d) πr²
6.The volume of a cylinder of radius 7 cm and height 10 cm is
(a) 490π cm³(b) 140π cm³(c) 70π cm³(d) 980π cm³
Section B: Short Answer Type Questions (2 Marks Each)
Show all steps clearly.
7.Write the formula for the volume of a sphere.
8.Find the total surface area of a cube of edge 5 cm.
9.Write the formula for the curved surface area of a cone.
10.Find the volume of a cuboid with length 10 cm, breadth 8 cm and height 6 cm.
11.Write the formula for the volume of a cylinder.
12.Find the total surface area of a hemisphere of radius 7 cm (take π = 22/7).
13.Write the formula for the volume of a cone.
14.Find the curved surface area of a cylinder of radius 7 cm and height 10 cm (take π = 22/7).
Section C: Numericals & Word Problems (3 Marks Each)
Apply the concepts to solve the problems. Show all working.
15.A rectangular box is 20 cm long, 15 cm wide and 10 cm high. Find its volume.
16.Find the volume of a sphere of radius 6 cm.
17.A cylindrical water tank has radius 7 m and height 4 m. Find the volume of water it can hold (take π = 22/7).
18.The radius of a sphere is doubled. By what factor does its volume increase?
19.A cubical water tank has a capacity of 27 m³. Find the length of its edge.
20.Find the total surface area of a cone whose slant height is 10 cm and base radius is 7 cm (take π = 22/7).
Answer Key
1. b) 2πrh
2. a) (4/3)πr³
3. b) 6a²
4. c) (1/3)πr²h
5. b) 3πr²
6. a) 490π cm³
7. Refer to solution guide.
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20. Refer to solution guide.
End of Worksheet
People Also Ask
What is the curved surface area of a cylinder?
2πrh, option (b) in this worksheet (Q1).
What is the volume of a sphere?
(4/3)πr³, option (a) in this worksheet (Q2).
What is the surface area of a cube of side a?
6a², option (b) in this worksheet (Q3).
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