Question

Find the volume of each of the given figure if volume = base area into height.

Answer 1

Answer:

The volume of (a) is x and the volume of (b) is 6y.

Answer 2

The volume of figure (a) is x³/2 and of figure (b) is 6y³.

Step-by-step explanation:

Case 1: Volume of given Figure (a)

The figure (a) is basically a right-angled triangular prism where

Base = $\frac{x}{2}$

Length = 2x

Height = x

The formula for the volume of figure (a) is given as,

Volume = Area of the triangle * length

⇒ Volume = [½ * base * height] * length

⇒ Volume = [½ * $\frac{x}{2}$ * x] * 2x

⇒ Volume = $\frac{x^3}{2}$

Case 2: Volume of Figure (b)

The figure (b) is basically a cuboid where

Length = 3y

Breadth = y  

Height = 2y

The formula for the volume of the cuboid of figure (b) is given as,

Volume = length * breadth * height

⇒ Volume = 3y * y * 2y

⇒ Volume = 6y³

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