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SAI International School
Sub – Mathematics
Class - V
Topic – Volume and Capacity
Sub-topic 11.3 : - Finding volume by area and height
Introduction:
We can find out the volume if the area of the surface and height of the 3D object are given.

Volume of cuboid when area and height are given
Volume of a cuboid = (length × breadth × height) cubic units.
= (l × b × h) cubic units.
(Since area = l × b) square units
Volume of a cuboid = (area of one surface × height) cubic units

Example 1: The area of the surface of the cuboid is 24 square metres and height is 9
metre. Find the volume of the cuboid.
Solution:
The area of the surface = 24 sq. m.
Height = 9 m.
Volume of a cuboid = (area of one surface × height) cubic units
= 24 sq. m X 9 m
= 216 cu. m.
Therefore, the volume of the cuboid is 216 cu. m.

Example 2: The area of the surface of the cuboid is 36 square cm and height is 9 mm.
Find the volume of the cuboid.
Solution:
The area of the surface = 36 square cm
Height = 9 mm = 0.9 cm
Volume of a cuboid = (area of one surface × height) cubic units
= 36 sq. cm X 0.9 cm
= 32.4 cu. cm.
Therefore, the volume of the cuboid is 32.4 cu. cm.

Volume of cube when area is given
Volume of a cube = (side × side × side) cubic units.
= (s × s × s) cubic units.
(Since area = s × s) square units
Volume of a cube = (area of one surface × side) cubic units

How to find side, when area is given:
Area = s x s
Side = square root of area
Then, we can find the volume of the cube.