[CLASS 9] Mathematics MCQs on Volume of a Sphere and Answers

Mathematics Multiple Choice Questions on “Volume of a Sphere”.

1. Volume of a sphere of radius r is equal to __________
a) (frac{4}{3} πr^3)
b) πr²h
c) (frac{1}{3}) πr²h
d) (frac{2}{3} πr^3)

Answer: a
Clarification: Volume of a sphere is (frac{4}{3}) π times the cube of a radius.
Therefore, volume of a sphere is equal to (frac{4}{3} πr^3).

2. Volume of a hemisphere of radius r is equal to __________
a) (frac{4}{3} πr^3)
b) πr²h
c) (frac{1}{3}) πr²h
d) (frac{2}{3} πr^3)

Answer: d
Clarification: Volume of a hemisphere is half the volume of a sphere.
We know that volume of a sphere of radius r is equal to (frac{4}{3} πr^3).
Therefore, volume of a hemisphere is equal to (frac{2}{3} πr^3).

3. What is the radius of a sphere having volume of 4851cm³? (Take π = (frac{22}{7}))
a) 9 cm
b) 11 cm
c) 10.5 cm
d) 11.3 cm

Answer: c
Clarification: We know that volume of a sphere of radius r is equal to (frac{4}{3} πr^3).
(frac{4}{3} πr^3) = 4851
(frac{4}{3} * frac{22}{7} * r^3) = 4851
(r^3 = frac{9261}{8})
Therefore, r = (frac{21}{2}) = 10.5 cm.

4. Curved surface area of a hemisphere is equal to 2772 cm², what is its volume? (Take π = (frac{22}{7}))
a) 19464 cm³
b) 19404 cm³
c) 19427 cm³
d) 19425 cm³

Answer: b
Clarification: We know that curved surface area of a hemisphere is equal to 2πr².
2πr² = 2772
r² = (frac{2772*7}{2*22}) = 441
Therefore, r = 21cm
Now, we know that volume of a hemisphere is equal to (frac{2}{3}) πr³.
Hence, V = (frac{2}{3}) πr³
= (frac{2*22*21*21*21}{3*7})
= 19404 cm³.

5. A hollow sphere of outer radius of 4 cm and thickness of 3 cm is to be made from metal. What is the total amount of metal required (in cm³) to make the sphere? (Take π = (frac{22}{7}))
a) 281
b) 264
c) 225
d) 227

Answer: b
Clarification: Outer radius r_o = 4cm
Inner radius r_i = outer radius – thickness
= 4 – 3
r_i = 1cm
This means that the sphere is hollow and volume of metal required = (frac{4}{3} πr_o^3 – frac{4}{3} πr_i^3)
= (frac{4}{3} π (4^3 – 1^3))
= (frac{4*22*63}{3*7})
= 264 cm³.

6. Cost of whitewashing a sphere is 1232₹ at the rate of 2₹/cm². What is the volume of a sphere? (Take π = (frac{22}{7}))
a) (frac{4324}{3})
b) (frac{4317}{5})
c) (frac{4312}{3})
d) (frac{4312}{7})

Answer: c
Clarification: Area of a sphere = (frac{Total ,cost ,of ,whitewashing}{Rate ,of ,whitewashing/cm^2})
= (frac{1232}{2})
= 616 cm²
We know that total surface area of a sphere = 4πr²
4πr² = 616
r² = (frac{616*7}{22*4})
= 49
Therefore, r = 7cm
Now, volume of a sphere = (frac{4}{3} πr^3)
= (frac{4}{3} * frac{22}{7}) * 7³
= (frac{4312}{3}).