# Mathematics Questions and Answers – Volume of a Cylinder

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This set of Mathematics Multiple Choice Questions & Answers (MCQs) focuses on “Volume of a Cylinder”.

1. Volume of a cylinder having radius r and height h is given by __________
a) r * h2
b) h * r2
c) πr2h
d) $$\frac{1}{3}$$πr2h

Explanation: Volume of a cylinder can be given by multiplying base area with its height.
Hence, volume of a cylinder having radius r and height h is equal to πr2h where πr2 is base area and h is height.

2. A cylinder has radius of 7cm and its volume is 1540cm3, what is the height of the cylinder? (Take π = $$\frac{22}{7}$$)
a) 10cm
b) 14cm
c) 11cm
d) 15cm

Explanation: Volume of a cylinder having radius r and height h is equal to πr2h.
πr2h = 1540
$$\frac{22}{7}$$ * 7 * 7 * h = 1540
h = 10cm.

3. A cylinder has volume of 176cm3 and height equal to 14cm, what is the diameter of the cylinder? (Take π = $$\frac{22}{7}$$)
a) 6cm
b) 8cm
c) 2cm
d) 4cm

Explanation: Volume of a cylinder having radius r and height h is equal to πr2h.
πr2h = 176
$$\frac{22}{7}$$ * 14 * r2 = 176
r2 = 4
Therefore, r = 2cm
We know that diameter = 2 * radius
= 2 * 2
= 4cm.

4. A glass of cylindrical shape has radius of 3.5cm and height equal to 8cm. A water jug has a volume equal to 1540cm3. How many times the water has to be poured from glass to fill the jug completely? (Take π = $$\frac{22}{7}$$)
a) 6
b) 5
c) 4.5
d) 4

Explanation: Volume of a cylindrical glass = πr2h
= $$\frac{22}{7}$$ * 3.5 * 3.5 * 8
= 308cm3
Volume of a water jug = 1540cm3
Therefore, number of times the water has to be poured from glass to fill the jug completely
= $$\frac{Volume \,of \,a \,water \,jug}{Volume \,of \,a \,cylindrical \,glass} = \frac{1540}{308}$$
= 5.

5. Cylindrical pillars are to be made for a flat whose radius is 15cm and height is 3.5m. What is the total amount of concrete (in cm3) required to make 15 identical pillars? (Take π = $$\frac{22}{7}$$)
a) 3513600
b) 3712500
c) 4125300
d) 3917800

Explanation: Volume of one cylindrical pillar = πr2h
= $$\frac{22}{7}$$ * 15 * 15 * 350
= 247500cm3
Hence, total volume of 15 pillars = 15 * 247500
= 3712500cm3
Therefore, the total amount of concrete required to make 15 identical pillars = 3712500cm3.

6. A cylinder has a base area equal to 21cm2 and height equal to 11cm. What is the volume of the cylinder? (Take π = $$\frac{22}{7}$$)
a) 230cm3
b) 220cm3
c) 225cm3
d) 231cm3

Explanation: We know that base area of a cylinder is equal to πr2.
Volume of a cylinder = πr2h
= 21 * 11
= 231cm3.

7. A steel pipe has outer radius equal to 3cm and inner radius equal to 2cm. Its length is equal to 5m. What is the mass of the pipe if one cm3 of steel is 8.05 gram? (Take π = $$\frac{22}{7}$$)
a) 63.25 kg
b) 65 kg
c) 67 kg
d) 61 kg

Explanation: Let the outer radius = ro = 3cm
Inner radius = ri = 2cm
Height (here length) = l = 5m = 500cm
Volume of pipe = π * (ro 2 – ri 2) * l
= $$\frac{22}{7}$$ * (32 – 22) * 500
= 7857.14cm3
Mass of 1cm3 is 8.05 gram
Therefore, mass of 7857.14cm3 is equal to 8.05 * 7857.14
= 63249.97gm
≈ 63250 gm
= 63.25 kg. 