Volume and Surface Area Questions and Answers - Set 01

Practice Test: Question Set - 01

1. The altitude of a circular cylinder is increased 6 times and the base area is decreased to one-ninth of its volume. The factor by which the lateral surface of the cylinder increases is?
    (A) 1/2 m
    (B) 2/3 m
    (C) 3/2 m
    (D) 2 m

2. A circular pipe is to be so designed that water flowing through it at a velocity of 4 mts per min is collected at its open end of 11 cubic mts per min, what should be the inner radius of the pipe?
    (A) 1/2 m
    (B) 1/√2 m
    (C) √2 m
    (D) 2 m

3. Three solid gold spherical beads of radii 3 cm and 5 cm respectively are melted into one spherical bead. Its radius in cm is:
    (A) 5
    (B) 4
    (C) 7
    (D) 6

4. The diameter of the base circle of a cone is equal to 54 cm and the generator is 13 cm. The area of the axial section will be:
    (A) 240 cm²
    (B) 120 cm²
    (C) 60 cm²
    (D) 32.5 cm²

5. A plane is drawn parallel to the base of a right circular cone dividing the altitude in the ratio of 2:1 to chop off the conical part. The chopped off conical part is taller than the remaining portion. The ratio of the volumes of the chopped off part and the remaining part is:
    (A) 1 : 26
    (B) 2 : 25
    (C) 4 : 23
    (D) 8 : 19

6. The area of the diagonal section of a cube is equal to 4√2 cm². The edge of the cube is:
    (A) 4 cm
    (B) 3 cm
    (C) 2√2 cm
    (D) 2 cm

7. The base diameter and the height of a right circular cone are each increased by 100%. The volume of the cone is increased by:
    (A) 100%
    (B) 200%
    (C) 400%
    (D) 700%

8. If a rectangular paper of length 30 cm and width 12 cm is rolled to form a cylinder with height equal to the width of the paper, then its base radius is:
    (A) 18/π cm
    (B) 15/π cm
    (C) 15π/2 cm
    (D) 9π/2 cm

9. If ‘h’ be the height and ‘α’ be the semi vertical angle of a right circular cone, then its volume is given by:
    (A) πh3 tan²α / 3
    (B) πh² tan²α / 3
    (C) πh3 tan3α / 3
    (D) πh² tan3α / 3

10. If the edges of a cuboid are 3 cm, 4 cm and 12 cm, then the length of its diagonal is:
    (A) √5 cm
    (B) √19 cm
    (C) 12 cm
    (D) 13 cm

11. The area of a rhombus with side 50 dm and one of the diagonals 80 dm is:
    (A) 1600 dm²
    (B) 500 dm²
    (C) 1200 dm²
    (D) 2500 dm²

12. Volume of a right circular cylinder and the volume of a sphere (whose radius is same as that of cylinder) are equal, if the height of the cylinder is:
    (A) 4/5 times of its radius
    (B) 4/3 times of its radius
    (C) Equal to its radius
    (D) Equal to its diameter

13. The number of round that a wheel of diameter 7 m will make in going 4.4 km is:
    (A) 1000
    (B) 800
    (C) 2000
    (D) 100

14. A plot of land in the shape of a right angled isosceles triangle, the length of the hypogenous side is 50√2, the cost of fencing is Rs. 3 per meter. The cost of fencing the plot is:
    (A) Rs. 381
    (B) Rs. 341
    (C) Rs. 391
    (D) Rs. 371

15. A circle and a square have same area. Therefore, the ratio of the side of the square and the radius of the circle is:
    (A) √π : 1
    (B) 1 : √π
    (C) 1 : π
    (D) π : 1

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Volume and Surface Area:
Formula:                Volume and Surface Area Formulas
Solved Examples:  Solved Examples: Set 01
Practice Test:         Practice Test: 01     Practice Test: 02
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