Practice the problems of Math in Focus Grade 8 Workbook Answer Key Chapter 7 The Pythagorean Theorem to score better marks in the exam.

## Math in Focus Grade 8 Course 3 A Chapter 7 Answer Key The Pythagorean Theorem

### Math in Focus Grade 8 Chapter 7 Quick Check Answer Key

**Find the square of each number.**

Question 1.

3

Answer:

9,

Explanation:

Given number is 3 the square is 3^{2 }= 3 X 3 = 9.

Question 2.

\(\frac{1}{4}\)

Answer:

\(\frac{1}{16}\),

Explanation:

Given number is \(\frac{1}{4}\) the sqaure is

(\(\frac{1}{4}\))^{2 }= \(\frac{1}{4}\) X \(\frac{1}{4}\) =

\(\frac{1 X 1}{4 X 4}\) = \(\frac{1}{16}\).

Question 3.

-7

Answer:

49,

Explanation:

Given number is -7 the square is (-7)^{2 }= -7 X -7 = 49.

**Find the square roots of each number.**

Question 4.

16

Answer:

4,

Explanation:

Question 5.

64

Answer:

8,

Explanation:

Question 6.

400

Answer:

20,

Explanation:

**Find the cube of each number.**

Question 7.

\(\frac{1}{2}\)

Answer:

\(\frac{1}{8}\),

Explanation:

Given \(\frac{1}{2}\) the cube is (\(\frac{1}{2}\))^{3 }=

\(\frac{1}{2}\) X \(\frac{1}{2}\) X \(\frac{1}{2}\) =

\(\frac{1 X 1 x 1}{2X 2 X 2}\) =\(\frac{1}{8}\).

Question 8.

7

Answer:

343

Explanation:

Given 7 the cube is (7)^{3 }= 7 X 7 X 7 = 343.

Question 9.

11

Answer:

1331,

Explanation:

Given 11 the cube is (11)^{3 }= 11 X 11 X 11 = 1331.

**Find the cube root of each number.**

Question 10.

8

Answer:

2

Explanation:

Question 11.

27

Answer:

3

Explanation:

Question 12.

125

Answer:

5

Explanation:

**Use graph paper. Plot each pair of points on a coordinate plane. Connect the points to form a line segment and find its length.**

Question 13.

(3, 5) and (3, 9)

Answer:

The objective is to plot and connect point (-3, 1) and point(-3, -3) on a coordinate plane, then identify the length of the line that the two points create.

Note that to represent point (-3, 1), point out in which part of the graph does -3 and 1 meet. -3 is 3 units to the left of 0 and 1 is 1 unit up. Likewise, for point (-3, -3), point out in which part of the graph does -3 and -3 meet. The first -3 is 3 units to the left of 0 and the other -3 is 3 units down. Then, let O be the point (-3, 1), and P be the point (-3, -3).

To find the length of the line segment \(\overline{O P}\), get the absolute value of the difference of y-coordinate of point O to the y-coordinate of P since points O and P have the same x-coordinate which is -3. Then

length of \(\overline{O P}\) = |1 – (-3)|

= |1 + 3|

= 4

Therefore, the length of \(\overline{O P}\) is 4 units.

Question 14.

(3, -6) and (3, -9)

Answer:

The goal of this task is to plot and connect point (1, 2) and point (1, -1) on a coordinate plane, then identify the length of the line that the two points create.

Notice that to show point (1, 2), specify in which part of the graph does 1 and 2 meet. 1 is 1 unit to the right of 0 and 2 is 2 units up. Likewise, for point (1, -1), specify in which part of the graph does 1 and -1 meet 1 is 1 unit to the right of 0 and -1 is 1 unit down. Then, Let Q be the point (1, 2), and R be the point (1, -1).

To find the length of the line segment \(\overline{Q R}\), get the absolute value of the difference of y-coordinate of point Q to the y-coordinate of R since points Q and R have the same x-coordinate which is 1. Then

length of \(\overline{Q R}\) = |2 – (-1)|

= |2 + 1|

= 3

Therefore, the length of \(\overline{Q R}\) is 3 units.

Question 15.

(-4, 9) and (-8, 9)

Answer:

The target of this task is to plot and connect point (1, -3) and point (5, -3) on a coordinate plane, then identify the length of the line that the two points create.

Observe that to represent point (1, -3), point out in which part of the graph does 1 and -3 meet 1 is 1 unit to the right of 0 and -3 is 3 units down. Likewise, for point (5, -3), point out in which part of the graph does 5 and -3 meet 5 is 5 units to the right of 0 and -3 is 3 units down Then, let S be the point (1, -3), and T be the point (5, -3).

Now, to find the length of the line segment \(\overline{S T}\), get the absolute value of the difference of x-coordinate 1 of point S to the x-coordinate of T since points S and T have the same y-coordinate which is -3. Then

length of \(\overline{S T}\) = |1 – 5|

= |-4|

= 4

Therefore, the length of \(\overline{S T}\) is 4 units.

Question 16.

(-2, 5) and (8, 5)

Answer:

The objective of this task is to plot and connect point (-5, 3) and point (5, 3) on a coordinate plane, then identify the

length of the line that the two points create.

Note that to show point (-5, 3), specify in which part of the graph does -5 and 3 meet -5 is 5 units to the left of 0 and 3 is 3 units up. Likewise, for point (5, 3), specify in which part of the graph does 5 and 3 meet 5 is 5 units to the right of 0 and 3 is 3 units up. Then, let U be the point (-5, 3), and V be the point (5, 3).

Next, to determine the length of the Line segment \(\overline{U V}\), get the absolute value of the difference of x-coordinate of point U to the x-coordinate of V since points U and V have the same y-coordinate 3. Then

length of \(\overline{U V}\) = |-5 – (5)|

= |-5 + -5|

= |-10|

= 10

Therefore, the length of \(\overline{U V}\) is 10 units.

**Find the volume of each solid. Use 3.14 as an approximation for π. Round your answers to the nearest tenth if necessary.**

Question 17.

Answer:

Volume of cone **≈ **1206.37 cm^{3 },

Explanation:

Question 18.

Answer:

The volume of cylinder **≈**1206.37 cm^{3 },

Question 19.

Answer:

Volume of sphere is **≈**33.51 cm^{3},

Explanation:

Question 20.

Answer:

Volume of triangular prism is 35 cm^{3 },

Explanation:

Volume of triangular prism = area of cross-section X length,

5 cm^{2 }× 7 cm = 35 cm^{3}.

Question 21.

Answer:

Volume of Pyramid is 15 cm^{3},

Explanation: