Solved Problems on Mensuration

Let’s solve some example problems on mensuration.

Problem 1: Find the volume of a cone if the radius of its base is 1.5 cm and its perpendicular height is 5 cm.

Solution:

Radius of the cone, r = 1.5 cm

Height of the cone, h = 5 cm

∴ Volume of the cone, V = 13πr²h=13×227×(1.5)²×5= 11.79 cm³

Thus, the volume of the cone is 11.79 cm³. 

Problem 2: The dimensions of a cuboid are 44 cm, 21 cm, 12 cm. It is melted and a cone of height 24 cm is made. Find the radius of its base.

Solution:

The dimensions of the cuboid are 44 cm, 21 cm and 12 cm.

Let the radius of the cone be r cm.

Height of the cone, h = 24 cm

It is given that cuboid is melted to form a cone.

∴ Volume of metal in cone = Volume of metal in cuboid

⇒(1/3)πr²h=44×21×12             

 (Volume of cuboid=Length×Breadth×Height)

⇒(1/3)×(22/7)×r²×24=44×21×12

⇒r= √(44×21×12×21) / (22×24)

=21 cm

Thus, the radius of the base of cone is 21 cm.
 

Problem 3: The radii of two circular ends of frustum shape bucket are 14 cm and 7 cm. The height of the bucket is 30 cm. How many liters of water can it hold? (1 litre = 1000 cm³).

Solution:

Radius of one circular end, r1 = 14 cm

Radius of other circular end, r2 = 7 cm

Height of the bucket, h = 30 cm

∴ Volume of water in the bucket = Volume of frustum of cone
=(1/3)πh(r₁²+r₁r₂+r₂²)

=13×22/7×30×(142+14×7+72)

=13×22/7×30×343=10780 cm³

=107801000=10.780 L

Thus, the bucket can hold 10.780 litres of water.

Mensuration is a branch of mathematics concerned with the calculation of geometric figures and their parameters such as weight, volume, form, surface area, lateral surface area, and so on.

Let’s learn about all the mensuration formulas in maths.