Find the volume of each of the given figure if volume = base area × height.
Solution:
In figure (a) the base of the solid is a right angled triangle with a height 2x.
The area of the triangle is = 1/2 × base × height
Area of base triangle = 1/2 × (x/2) × (x) = x²/4
Height of the right angled triangular solid = 2x
Volume of the Solid = x²/4 × 2x = x³/2
The figure (b) is a cuboid with length = 3y; breadth = y and height = 2y
Volume of the cuboid = length × breadth × height
Volume of the cuboid = 3y × 2y × y = 6y³
The figure (c) is a solid with length = 2p; breadth = 2p and height = 2p
Volume of the solid = base area × height
= 2p × 2p × 2p = 8p³
✦ Try This: Find the volume of each of the given figure if volume = base area × height.
In figure (a) the base of the solid is a right angled triangle with a height 2x.
The area of the triangle is = 1/2 × base × height
Area of base triangle = 1/2 × (x) × (2x) = x²
Height of the right angled triangular solid = 4x
Volume of the Solid = x² × 4x = 4x³
The figure (b) is a cuboid with length = 3y; breadth = y and height = 2y
Volume of the cuboid = length × breadth × height
Volume of the cuboid = 3y × y/2 × 2y/3 = y³
☛ Also Check: NCERT Solutions for Class 8 Maths Chapter 11
NCERT Exemplar Class 8 Maths Chapter 11 Problem 86
Find the volume of each of the given figure if volume = base area × height.
Summary:
Volumes of the given solid shapes are (a) x³/2, (b) 6y³, (c) 8p³
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