Question

Find the volume of the figure: a prism of volume 15 with a pyramid of the same height cut out.

Answer 1

The volume of the figure is 10 cubic units, if a prism of volume 15 with a pyramid of the same height cut out.

Explanation:

The given is,

A prism of volume 15

A pyramid of the same height cut out

For the above question diagram is missing, so i attach the diagram.

Step:1

Ref the attachment,

Volume of figure = Volume of Prism - Volume of Pyramid....(1)

Step:2

From the given diagram,

Formula for volume of prism,

`V_(prism) = whl`......................(2)

Where, w - Width of the prism

h - Height of prism

l - Length of prism

From the given,

Volume, V = 15 cubic units

l = a

w = b

h = c

Equation (1) becomes,

15 = abc

c =
`(15)/(ab)`

Step:3

Volume of pyramid,
`V = (whl)/(3)`..........................(2)

where,

w - Width of pyramid

h - Height of pyramid

l - Length of pyramid

From the given,

l = a

w = b

h = c

From the volume of prism, h = c =
`(15)/(ab)`

Equation (2) becomes,

`V_(pyramid) = ((ab)/(3) )((15)/(ab ) )`

= 5

`V_(pyramid) = 5` cubic units

Step:4

Equation (1) becomes,

Volume of figure = 15 - 5

= 10 cubic units

Result:

The volume of the figure is 10 cubic units, if a prism of volume 15 with a pyramid of the same height cut out.