WORKSHEET ON CUBE ROOTS

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Evaluate each of the following:

1) ∛-27

2) ∛1/8

3) ∛27

4) - ∛1/64

5) ∛-8/27

6) ∛-1000

7) ∛-27/64

8) -∛-64

9) ∛-1/125

Solution

Problem 10 :

The volume of a cube-shaped compost bin is 27 cubic feet. What is the edge length of the compost bin?

Solution

Problem 11 :

The volume of a cube of ice for an ice sculpture is 64,000 cubic inches.

a. What is the edge length of the cube of ice?

b. What is the surface area of the cube of ice?

Solution

Problem 12 :

Solve the equation.

a) (3x + 4)³ = 2197

b) (8x³ − 9)³ = 5832

c) ((5x − 16)³ − 4)³ = 216,000

Solution

Problem 13 :

You bake a dessert in the baking pan shown. You cut the dessert into cube-shaped pieces of equal size. Each piece has a volume of 8 cubic inches. How many pieces do you get from one pan? Justify your answer.

Solution

Problem 14 :

The formula for volume of a pyramid is V = (1/3)ℓwh. The pyramid has a volume of 972 cubic inches. What are the dimensions of the pyramid?

Solution

Problem 15 :

There are three numbers that are their own cube roots. What are the numbers?

Solution

Answer Key

1) -3

2) 1/2

3) 3

4) -1/4

5) -2/3

6) -10

7) -3/4

8) 4

9) -1/5

10) side length of compost bin is 3 ft.

11) a) Side length of the cube is 40 inches

b) 9600 square inches.

12) a) x = 3

b) x = 3/2

c) x = 4

13) 32 pieces.

14) length = 18 inches, width = 18 inches and height = 9 inches

15) -1, 0 and 1 are the numbers which has their own cube roots.

Evaluate :

1) ∛1

2) ∛-1

3) ∛-27

4) ∛8

5) ∛-8

6) ∛64

7) ∛125

8) ∛-216

9) ∛-1000

10) ∛343

Solution

Problem 11 :

Find the value of the cube roots

∛(27 x 2744)

Solution

Problem 12 :

By which smallest number must 5400 be multiplied to make it a perfect cube?

Solution

Problem 13 :

Find the smallest number by which 16384 be divided so that the quotient may be a perfect cube.

Solution

Problem 14 :

Is 4096 a perfect cube? If yes, then what is the number whose cube root is 4096?

Solution

Problem 15 :

Find the smallest number by which 375 must be multiplied to obtain a perfect cube

Solution

Problem 16 :

Find the cube root of 0.008/0.125

Solution

Answer Key

1) 1

2) -1

3) -3

4) 2

5) -2

6) 4

7) 5

8) -6

9) -10

10) 7

11) 42

12) 5

13) 4

14) 4096 is a perfect cube and answer is 12.

15) 9

16) 0.4

Evaluate :

1) ∛(1/125)

2) ∛(-8/27)

3) ∛343/64

4) -∛1 91/125

5) ∛(1/64)

6) ∛3 3/8

7) ∛-216

8) ∛27/125

9) - ∛(343/1000)

10) ∛729/64

Solution

Answer Key

1) 1/5

2) -2/3

3) 7/4

4) -6/5

5) 1/4

6) 3/2

7) -6

8) 3/5

9) -7/10

10) 9/4

Problem 1 :

Calculate the volume of the cube if its surface is 150 cm².

Solution

Problem 2 :

The cube has a surface of 600 cm². What is its volume?

Solution

Problem 3 :

We make a box in the shape of a cube with an edge of 12 cm. how many cm² of sheet metal do we need to create a box if we do not make the lid?

Solution

Problem 4 :

If we reduce the length of the cube edge by 30%, this reduced cube has an area of 1176 cm². Specify the edge length and volume of the original cube.

Solution

Problem 5 :

How can you change the edge length of a cube so that the volume is reduced by 40%?

Solution

Problem 6 :

A pyramid with a square base has a volume of 120 cubic meters and a height of 10 meters. Find the side length of the square base.

Solution

Problem 7 :

A pyramid with a square base has a volume of 912 cubic feet and a height of 19 feet. Find the side length of the square base.

Solution

Problem 8 :

A cube with a surface area of 96 square centimeters is shown. Eight cubes like the one shown are combined to create a larger cube. What is the volume, in cubic centimeters, of the new cube?