Question

The ratio of the corresponding linear measures of two similar triangular prisms is 2 to 5. The larger triangular prism has a volume of 150 cubic centimeters. Find the volume of the smaller triangular prism.

Answer 1

Given :

The ratio of the corresponding linear measures of two similar triangular prisms = 2 : 5

The volume of Larger triangular prism = $V_L$ = 150 cubic cm

To Find :

The volume of the smaller triangular prism.

Solution :

Let The volume of the smaller triangular prism = $V_S$

Let The linear height of larger prism = $L_l$ = 5 l

And,

The linear height of smaller prism = $L_s$ = 2 l

∵ The volume of the triangular prism = Area of base × linear height

For Larger triangular prism

 $V_L$ =  Area of base × $L_l$

i.e   150 cubic cm = Area of base × 5 l

Or,  Area of base = $\dfrac{150}{5l}$                   .............1

Again

For smaller triangular prism

 $V_S$ =  Area of base × $L_s$

Or,  =  Area of base × 2 l

       = $\dfrac{150}{5l}$   × 2 l                          ( From eq 1 )

       = 30 × 2

       = 60 cm³

Hence, The volume of the smaller triangular prism is 60 cubic centimeters   Answer