MATH Integrated Math I  - Unit 24: Volume
For all answers in this unit, round to the nearest tenth, when necessary unless otherwise directed. In addition, label answers properly. For example: 64 cubic feet would be written as 64 cu ft. Volume of Prisms

1) Standard measures of volume are _______________ units

2) What is the volume of the rectangular prism? (Hint: 1 1/2 may be written as 1.5)

250 character(s) left

3) What is the volume of the cube?

250 character(s) left

4) What is the volume of the triangular prism?

250 character(s) left

5) What is the volume of the triangular prism?

250 character(s) left

6) What is the volume of a rectangular prism with a length of 2 feet, a width of 3 feet, and a height of 8.5 feet?

250 character(s) left

7) What is the volume of the hexagonal prism?

250 character(s) left

The volume of the left cube represents 1 cubic yard (1 × 1 × 1).  The right cube is the same size; however, the unit of measure is written in feet (1 foot = 3 feet).   Notice that the VOLUME of the cube in cubic feet is (3)(3)(3) or 27 cubic feet.   Use this same principal to calculate the conversion factors in the next two problems.

8) How many cubic inches are in one cubic foot? (Hint:  1 foot = 12 inches)

9) How many cubic centimeters are in one cubic meter? (Hint:  1 meter = 100 centimeters)

Volume of Cylinders

10) What is the volume of a cylinder with a radius of 3.7 inches and a height of 15 inches?

250 character(s) left

11) What is the volume of a cylinder with a radius of 10.7 yards and a height of 4.4 yards?

250 character(s) left

12) What is the volume of the cylinder that has a DIAMETER of 8.3 feet and a height of 28.2 feet? (Note: Adjust the diameter to a radius to use in the volume formula.)

250 character(s) left

13) What is the height of a cylinder that has a radius of 5 inches and the volume is 402.7 cubic inches?

250 character(s) left

14) Logan’s mom bought her a circular-shaped baby pool that is 5 feet in diameter and 1.8 feet deep. About how much water will the pool hold?

250 character(s) left

Volume of Cones and Pyramids

15) The volume of a cone is what fractional part of the volume of a cylinder with the same radius and height?

16) What is the volume of the cone?

250 character(s) left

17) What is the volume of a cone that has a diameter of 14 centimeters and a height of 6 centimeters? (Hint:  Find the radius first, then solve the problem.)

250 character(s) left

18) What is the volume of a cone that has a diameter of 34.7 millimeters and a height of 22.8 millimeters?  Adjust the diameter to a radius to use in the formula.

250 character(s) left

19) What is the volume of the triangular pyramid? 

250 character(s) left

20) What is the volume of a square pyramid that has a base edge of 6.8 centimeters and a height of 13.6 centimeters?  (Note: The base of the pyramid is a square. The formula for calculating the area of a square is A = s^2.)

250 character(s) left

21) What is the volume of the octagonal pyramid? (Note:  The base of this pyramid is an octagon.)

250 character(s) left

Volume of Spheres

22) What is the volume of a sphere with a radius of 2.25 inches?

250 character(s) left

23) What is the volume of a sphere with a diameter of 10.6 meters? Adjust the diameter to a radius to use in the formula.

250 character(s) left

Changing Dimensions

24) The edge of the larger cube is twice as long as the edge of the smaller cube. How many times larger is the volume of the larger cube than the volume of the smaller cube? (Note:  To compare the volumes, divide the larger volume by the smaller volume.)

25) The radius of the larger sphere is 3 times as long as the radius of the smaller sphere. How many times larger is the volume of the bigger sphere than the volume of the smaller sphere?

26) What is the effect on the volume of a sphere when the diameter is doubled? (Image: Idea go / FreeDigitalPhotos.net)

Volume of Complex Solids

Many objects in real-life are made up of more than one type of solid. Such figures are called COMPLEX SOLIDS. To find the volume of a complex solid, separate the figure into basic solids.

27) A wooden block has a hole drilled through it as shown below. What is the volume of the block? (Note:  The volume of the cylindrical hole is removed from the volume of the block.)

250 character(s) left

28) What is the volume of the treasure chest shown below? [Recall that the formula for the area of a trapezoid is A = (1/2) h (a + b).]

250 character(s) left

Mixed Review

29)

When filled to maximum capacity, a silo can hold about 8000 cubic feet of corn. The circumference (C) of the silo is about 37.68 feet and the height of the silo is 40 feet. What is the radius and volume of the cylinder? Express the volume rounded to the nearest whole foot. (Recall that the formula for finding the circumference of a circle is C = 2 pi r.)


250 character(s) left

30) Before B.J. buys the tent shown in the ad below, he decides to calculate the maximum amount of people who could occupy the tent. If the average person requires at least 40 cubic feet of space, how many people could fit in the tent?

31) In the given  figure, cubes are stacked in a corner of a container. How many cubes are in the bottom layer?

32) Lori sliced an edge from an octagonal prism as shown in the figure below. Points A, B, and C are three of the eight vertices on the front face of the octagon. What type of three-dimensional figure was cut from the prism?

33) Betty is constructing a wading pool to put the final touches on her landscaping project.  For the pool, she has a space of 5 feet by 7 feet by 3.2 feet. The diameter of the wading pool will be 4.6 feet.About how many cubic feet of water will the wading pool hold? Express the answer rounded to the nearest tenth of a foot. (Note:  Not all of the numbers given in the picture will be used to answer the question.)

250 character(s) left

34) If you were directed by your school to complete Offline Activities for this course, please enter the information on the Log Entry form.
No offline activities found
0 Hour(s) & 0 Minute(s)

If you are NOT required to complete Offline Activities for this course, please check the box below.





Attachments
There are no attachments

 Attach a File