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Worksheet Grade 8 Math

Quarrymoor Reuse Tanks: Finding a Missing Dimension From Volume

A grade 8 worksheet on a fictional reclaimed water site where students find cylinder, cone, and sphere volumes and then work backward to a missing depth or radius.

Objectives

  1. Students will compute the volume of a cylinder, a cone, and a sphere from given dimensions.
  2. Students will solve for a missing depth or radius when the volume of a tank is known.
  3. Students will convert a volume in cubic feet to gallons using a given conversion factor.

Vocabulary

Key words: cylinder, cone, sphere, radius, cubic foot

Teacher overview

The fictional Quarrymoor Reuse Site cleans wastewater a second time so it can be used to irrigate a golf course and two ball fields, and the site stores that reclaimed water in tanks of three shapes. Some tanks are already built, so their volume has to be computed from their dimensions. Others are still being designed, so the required volume is known and a dimension has to be found. A common error on this worksheet is squaring the diameter instead of the radius, which makes every cylinder answer four times too large.

Quarrymoor Reuse Tanks: Finding a Missing Dimension From Volume — Grade 8 Math
Name: ____________________________ Date: ______________

Student Worksheet

Use 3.14 for pi. One cubic foot holds 7.48 gallons. Round each answer to the nearest whole number unless the numbers come out exact. All tanks below are at the fictional Quarrymoor Reuse Site.

  1. The main storage tank is a cylinder. It is 30 feet across and 16 feet deep. Find its volume in cubic feet.
  2. The main storage tank holds 11,304 cubic feet. How many gallons is that?
  3. A new cylinder tank must hold 25,120 cubic feet. It will be 40 feet across. How deep must it be?
  4. A third cylinder tank is 10 feet deep. It holds 12,560 cubic feet. What is its radius?
  5. A sludge hopper is a cone. It is 12 feet across the top and 9 feet tall. Find its volume in cubic feet.
  6. A second cone hopper must hold 452.16 cubic feet. Its radius is 6 feet. How tall must it be?
  7. A pressure tank is a sphere with a radius of 6 feet. Find its volume in cubic feet.
  8. A smaller sphere tank holds 113.04 cubic feet. What is its radius?
  9. The sludge hopper in item 5 holds 339.12 cubic feet. How many gallons is that?
  10. Two cylinder tanks are both 16 feet deep. The second tank is twice as wide across as the first. How many times as much water does the second tank hold? Explain your reasoning.

From Water for Schools (waterforschools.org). This material is in the public domain (CC0) and may be copied, edited, and shared freely.

Answer Key
  1. Answer: 11,304 cubic feet. The radius is half of 30, or 15 feet. Then 15 squared is 225, and 3.14 times 225 is 706.5. Multiply by the depth: 706.5 times 16 equals 11,304 cubic feet.
  2. Answer: 84,554 gallons. Multiply 11,304 cubic feet by 7.48 gallons per cubic foot to get 84,553.92, which rounds to 84,554 gallons.
  3. Answer: 20 feet. The radius is half of 40, or 20 feet, and 20 squared is 400. Then 3.14 times 400 is 1,256 square feet of floor. Divide the volume by that area: 25,120 divided by 1,256 equals 20 feet.
  4. Answer: 20 feet. Divide the volume by pi and by the depth: 3.14 times 10 is 31.4, and 12,560 divided by 31.4 is 400. The radius squared is 400, so the radius is the square root of 400, or 20 feet.
  5. Answer: 339.12 cubic feet. The radius is half of 12, or 6 feet, and 6 squared is 36. Then 3.14 times 36 is 113.04, and 113.04 times 9 is 1,017.36. Divide by 3 to get 339.12 cubic feet.
  6. Answer: 12 feet. The radius squared is 36, and 3.14 times 36 is 113.04. One third of 113.04 is 37.68. Divide the volume by that: 452.16 divided by 37.68 equals 12 feet.
  7. Answer: 904.32 cubic feet. The radius cubed is 6 times 6 times 6, or 216. Then 3.14 times 216 is 678.24. Multiply by 4 to get 2,712.96, then divide by 3 to get 904.32 cubic feet.
  8. Answer: 3 feet. Multiply the volume by 3 to get 339.12, then divide by 4 to get 84.78, then divide by 3.14 to get 27. The radius cubed is 27, so the radius is 3 feet.
  9. Answer: 2,537 gallons. Multiply 339.12 cubic feet by 7.48 gallons per cubic foot to get 2,536.6176, which rounds to 2,537 gallons.
  10. Answer: 4 times as much. Volume depends on the radius squared, and doubling the width doubles the radius. Since 2 squared is 4, the second tank holds four times the water even though it is only twice as wide.

Differentiation

Support

Give these students a formula card with the three volume formulas written out and a worked example of each, and mark items 1, 5, and 7 as the required set. Provide the reminder "cut the width in half first" printed above the cylinder items, since the radius step causes most of the errors.

Extension

Ask students to design a fourth tank for the site that holds exactly 15,700 cubic feet, choosing its shape and every dimension, and to show two different sets of dimensions that both work. Have them explain which set uses less floor space and why a plant might care.

ELL supports

Provide a labeled drawing of each shape with the radius, diameter, and depth marked in different colors, and keep the word pairs "across the top" and "diameter," "half of across" and "radius" posted. Allow students to record their steps as a labeled diagram before writing sentences.

Extensions

Have students measure a cylindrical container from home or the classroom, compute its volume in cubic inches, and then check the result against the volume printed on the label, explaining any difference in terms of rounding or the shape of the container's base.