Download Volume of Pyramids

Name ______________________________
Volume of Pyramids
Module 3
Learning Target: I can use the volume formula for a pyramid.
Opening Exercise
1. The lateral faces of a regular pyramid are composed of
1) squares
2) rectangles
3) congruent right triangles
4) congruent isosceles triangles
2. Which piece of paper can be folded into a pyramid?
1)
3)
2)
4)
Volume of Pyramids
Pyramids are three dimensional closed surfaces. The vertex of a pyramid is the point opposite the
base of the pyramid. The base of a regular pyramid is a regular polygon, and the lateral faces are
congruent isosceles triangles. The slant height of a regular pyramid is the distance from the vertex to
the midpoint of an edge of the base. The altitude of a pyramid is the perpendicular segment from the
vertex to the plane of the base.
1. A regular pyramid is shown below. Find the volume of the pyramid to the nearest cubic unit.
2. Determine the volume of the pyramid.
3. A square pyramid has a volume of 245 in3 . The height of the pyramid is 15 in. What is the area of
the base of the pyramid? What is the length of one side of the base?
4. The base of a pyramid is a rectangle with a width of 12 cm and a length of 22 cm. Find, in
centimeters, the height of the pyramid if the volume is 2552 cm3.
Name ______________________________
Volume of Pyramids
Module 3
Problem Set
1. Find the volume of a pyramid whose base is a square with edge length 3 and whose height is
also 3.
2. A pyramid has volume 24 and height 6. Find the area of its base.
3. A regular pyramid has a square base with a side of 14 meters. The height of the pyramid is 48
meters. What is the volume of the pyramid in cubic meters?
4. Identify the solid shown, and find its volume.
5. A regular pyramid with a square base is shown in the diagram below. A side, s, of the base of the
pyramid is 12 meters, and the height, h, is 42 meters. What is the volume of the pyramid in cubic
meters?
6. Gold has a density of 19.32 g/cm3 . If a square pyramid has a base edge length of 5 cm, height
of 6 cm, and a mass of 942 g, is the pyramid in fact solid gold? If it is not, what reasons could explain
mass
why it is not? Recall that density can be calculated with the formula density = volume.
Name ______________________________
Volume of Pyramids
Module 3
Exit Ticket
1. Find the volume of the right rectangular pyramid shown.
2. The base of a pyramid is a rectangle with a width of 6 cm and a length of 8 cm. Find, in
centimeters, the height of the pyramid if the volume is 288 𝑐𝑚3.