A rectangular pyramid fits exactly on top of a rectangular prism. The prism has a length of 15 cm, a width of 5 cm, and a height of 7 cm, and the pyramid has a height of 13 cm. Find the volume of the composite space figure.
We will be adding the volume of a rectangular prism and the volume of a pyramid for finding the volume of the composite space figure.
Answer: The volume of the composite space figure is 850cm³.
Let's find the volume of the composite space figure step by step.
Explanation:
Look at the figure of a composite space shown below.
Given:
Length of a pyramid (l\(_\text{py}\) ) = 15 cm
Width of a pyramid (w\(_\text{py}\) ) = 5 cm
Height of a pyramid (h\(_\text{py}\) ) = 7 cm
It is given that the rectangular pyramid fits exactly on top of the prism, the length and width of the prism are the same for the base of the pyramid.
So, Length of a prism (l\(_\text{pr}\)) =15 cm, width of a prism (w\(_\text{pr}\)) = 5cm and height of a prism (h\(_\text{pr}\)) = 13 cm
Volume of Prism (Vpr) = l\(_\text{pr}\) × w\(_\text{pr}\) × h\(_\text{pr}\)
⇒ V\(_\text{pr}\) = 15 cm × 5 cm × 7 cm
⇒ V\(_\text{pr}\) = 525 cm³ ....(eq 1)
Volume of Rectangular Pyramid V\(_\text{py}\) = (l\(_\text{py}\) × w\(_\text{py}\) × h\(_\text{py}\) ) / 3
⇒ V\(_\text{py}\) = (15 × 5 × 13) ÷ 3
⇒ V\(_\text{py}\) = 325 cm³ ....(eq 2)
From 1 and 2, Volume of composite space,
Volume of composite space = Volume of prism + Volume of Pyramid
⇒ V = 525 cm³ + 325 cm³ = 850 cm³
⇒ V = 850 cm³
We can calculate the volume of the prism by using the volume of a rectangular prism calculator.
Also, we can calculate the volume of the pyramid by using the volume of the rectangular pyramid calculator.