Name:________________________________________________________ Date:_________ Period:_______
Chapter 9: 3-D Figures
Topic 3: Volume Day 1
Volume:
______________________________ is described as the amount of space inside a figure. It is used in threedimensional objects and can be represented as the amount of space an object takes up. Volume
always uses ______________ units (or _______________). It is important not to mix up units when solving
volume, area, and perimeter problems.
Volume Formulas:
All of these formulas need to be memorized.
Cube:
Cone:
____________________
____________________
Rectangular Prism:
Sphere
____________________
____________________
Any Prism:
Pyramid:
____________________
____________________
Cylinder:
____________________
Where B is the area of the base.
Examples:
1.) A prism has a trapezoidal base with parallel sides measuring 12 inches and 8 inches. The
parallel sides are 4 inches apart. The height of the trapezoidal prism is 6 inches. Find its
volume.
2.) The height of a cylinder is 16 cm and the diameter of its base is 14 cm. In cubic inches, find the
volume of the cylinder.
3.) A regular pyramid has a height of 12 cm and a square base. If the volume of the pyramid is
256 cubic centimeters, how many centimeters are in the length of one side of its base?
(1) 8
(2) 16
(3) 32
(4) 64
4.) A right prism has a square base with an area of 12 square meters. The volume of the prism is
84 cubic meters. Determine and state the height of the prism, in meters.
5.) Two prisms with equal altitudes have equal volumes. The base of one prism is a square with a
side length of 5 inches. The base of the second prism is a rectangle with a side length of 10
inches. Determine and state, in inches, the measure of the width of the rectangle.
6.) The volume of a sphere is
500𝜋
3
in3. What is the length of the radius?
7.) Determine the volume of the prism below. It is a regular prism with a right triangular base.
8.) Use the diagram below to answer the following questions. All answers must be exact.
(a) Find the radius of base.
(b) Find the volume of the cone.
9.) The volume of a cylinder is 12,566.4 cm3, The height of the cylinder is 8 cm. Find the radius of
the cylinder to the nearest tenth of a centimeter.
10.) The volume of a sphere is approximately 44.6022 cubic centimeters. What is the radius of
the sphere, to the nearest tenth of a centimeter?
(1) 2.2
(2) 3.3
(3) 4.4
(4) 4.7
Name:________________________________________________________ Date:_________ Period:_______
Volume Day 1: Homework
1.) A rectangular prism has a base with a length of 25, a width of 9, and a height of 12. A second
prism has a square base with a side of 15. If the volumes of the two prisms are equal, what is the
height of the second prism?
(1) 6
(2) 8
(3) 12
(4) 15
2.) A cylinder has a height of 7 cm and a base with a diameter of 10 cm. Determine the volume, in
cubic centimeters, of the cylinder in terms of 𝜋.
3.) The diameter of a sphere is 15 inches. What is the volume of the sphere, to the nearest tenth of
a cubic inch?
(1) 706.9
(2) 1767.1
(3) 2827.4
(4) 14,137.2
4.) The volume of a rectangular prism is 144 cubic inches. The height of the prism is 8 inches.
Which measurements, in inches, could be the dimensions of the base?
(1) 3.3 by 5
(2) 2.5 by 7.2
(3) 12 by 8
(4) 9 by 9
5.) A packing carton in the shape of a triangular prism is shown in the diagram. What is the
volume, in cubic inches, of this carton?
(1) 20
(2) 60
(3) 120
(4) 240
6.) 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 on side of the base?
7.) A triangular prism has an isosceles right triangle base with a hypotenuse of √32 and a prism
height of 15. A square prism has a height of 15 and its volume is equal to that of the triangular
prism. What are the dimensions of the square base?
Review Questions:
8.) In ∆𝐴𝐵𝐶, 𝑚∠𝐴 = 𝑥, 𝑚∠𝐵 = 2𝑥 + 2, and 𝑚∠𝐶 = 3𝑥 + 4. What type of triangle is ∆𝐴𝐵𝐶?
9.) Which transformation is not always isometry?
(1) rotation
(3) reflection
(2) dilation
(4) translation
10.) Lines j and k intersect at point P. Line m is drawn so that it is perpendicular to lines j and k
at point P. Which statement is correct?
(1) Lines j and k are in perpendicular planes.
(2) Line m is in the same plane as lines j and k.
(3) Line m is parallel to the plane containing lines j and k.
(4) Line m is perpendicular to the plane containing lines j and k.