Download 10-12. Find the cube root of the following numbers

Lesson 10.1.1
HW: 10-12 to 10-17
Learning Target: Scholars will use their knowledge of how to find the volume of a cube given a side
length and to find the side length when given the volume.
You have previously calculated the volumes and surface areas of cubes (and, more generally, prisms)
using the lengths of the sides. But what if you wanted to reverse this process? In this lesson, you will
learn how to determine the length of the side of a cube when you already know the volume. You will
learn about a new operation, which is similar to the square-root operation, that will help you do this.
10-2. Find the surface area and the volume of the cube in problem 10-1. Show your
steps.
10-3. A different cube has a side of length 5. Write two expressions that would represent how to find the
volume of the cube. One expression should use exponents.
10-4. Now reverse the process. If you know the volume, how long is the side? Given the volumes of
different cubes below, work with your team to find the length of a side of each cube.
1.
2.
3.
4.
8 un3
125 m3
1000 ft3
40 in.3
10-5. In problem 10-4, did you find the solution by guessing and checking, or did you find a special key
on your calculator that helped?
10-6. If s = the length of a side of a cube, then s3 or “s cubed” represents the volume of the cube. If the
volume of the cube is 64 cubic units, write an equation (using s) stating that volume is 64 cubic units.
10-7. In Chapter 9, you solved equations with squares, such as x2 = 16, by using the square-root operation,
. To solve equations with cubes, such as x3 = 64, you need an operation that undoes cubing. You
need the operation called cube root. It uses the symbol
. Find the cube-root key on your
calculator. Different calculators perform this operation in different ways, so figure out how to do this on
your calculator and then find
to get the solution to x3 = 64.
10-8. If you have not already done so, use the
problem 10-4.
key on your calculator to check your answers for
10-9. Just like with perfect squares and square roots, cube roots of perfect cubes are positive
integers. Some of them are listed below.
Cube roots of non-perfect cubes like
are irrational numbers. Without a calculator,
you can approximate the cube root to be between consecutive integers, as you did with square
roots. Look at the example below.
Approximate each of the following cube roots between consecutive integers. Write each answer in the
same way as the above example.
a.
b.
c.
10-12. Find the cube root of the following numbers. Use your calculator as needed and round any
decimal answers to the nearest hundredth. Identify each answer as a rational or irrational number.
1. 1728
2. 54
3. 0.125
d.
10-13. Given that the volume of a certain cube is 125 cubic inches, find the dimensions given below.
4. Find the length of one side of the cube.
5. Find the surface area of the cube.
10-14. Find the area and perimeter of the shape below. Show your steps.
10-15. Change each number below from a decimal to an equivalent fraction. For help with repeating
decimals, review the Math Notes box from Lesson 9.2.4.
1. 0.72
2.
3. 0.175
4.
10-16. Johanna is planting tomatoes in the school garden this year. Tomato plants come in packs
of 6. She needs 80 plants in the garden and already has 28. How many packs of plants will she need?
10-17. Solve the following equations for the given variable.
5. 3x + (−4) = 2y + 9 for y
6. 12 =
x for x
7.
for x
8.
for y
Lesson 10.1.1




10-1. Painting or wrapping the cube would need information about surface area. Filling
the cube with any materials would need information about volume.
10-2. V = 27 ft3, SA = 54 ft2
10-3. 5 · 5 · 5 or 53
10-4. See below:
1. 2 units
2. 5 m
3. 10 ft


4. ≈ 3.42 in
10-5. Probably using guess and check but some may know about cube roots.
10-6. s3 = 64 cubic units


10-7.
=4
10-9. See below:
1.
2.
3.

4.
10-10. ≈ 192.6 m

10-12.
1.
2.
3.

10-13. See below:
1. 5 inches
2. 150 sq inches

10-14. Triangle =
, rectangle= (21.25)(7.6) = 161.5m2, total area= 199.5
2
m , hypotenuse of triangle is 12.56 m, so perimeter = 72.66m.

10-15. See below:
See below:
12, rational
3.78, irrational
0.5, rational
1.
2.
3.
4.

10-16. Possible equation: 6p + 28 = 80, where p = packs of plants, p = 8
are needed.
, so 9 packs

10-17.
1.
2.
3.
4.
See below:
y = 1.5x − 6.5
x = 14
x = 114