This handy Math in Focus Grade 5 Workbook Answer Key Chapter 15 Surface Area and Volume provides detailed solutions for the textbook questions.

## Math in Focus Grade 5 Chapter 15 Answer Key Surface Area and Volume

**Math Journal**

This rectangular container is \(\frac{2}{5}\)-filled with water.

How much more water is needed to increase the height of the water level to 3 centimeters?

Show two methods of solving this problem. Which method do you prefer? Why?

Answer:

Given rectangular tank has volume 8 cm X 10 cm X 5 cm = 400 cm^{3},

Method 1:

Knowing the volume of tank and water filled in it

as the rectangular container is \(\frac{2}{5}\)-filled with water.

\(\frac{2}{5}\) X 400 cm^{3 }= 160 cm^{3}, filled with water.

as 1 cubic centimeter is equal to 1 milliliters,

**Put on Your Thinking Cap!**

**Challenging Practice**

Question 1.

A rectangular tank is half-filled with water.

Another 650 cubic centimeters of water are needed to make it \(\frac{3}{5}\) full.

How much water will be in the tank when it is \(\frac{3}{5}\) full?

Answer:

3,900 cubic centimeters of water will be in the tank when it is \(\frac{3}{5}\) full,

Explanation:

Given a rectangular tank is half-filled with water.

Another 650 cubic centimeters of water are needed to make it \(\frac{3}{5}\) full.

Let x cubic centimeters of water so \(\frac{1}{2}\)x + \(\frac{3}{5}\)x = 650 cm^{3} + x,

\(\frac{5x + 6x}{10}\) = 650 cm^{3} + x,

\(\frac{11x}{10}\) = 650 cm^{3} + x,

11 x = 10 X (650 cm^{3} + x),

11 x = 6500 cm^{3} + 10 x,

11x – 10 x = 6,500 cm^{3},

x = 6,500 cm^{3},

So, water will be in the tank when it is \(\frac{3}{5}\) full is

\(\frac{3}{5}\) x 6,500 cm^{3 }= \(\frac{3 X 6,500}{5}\) cm^{3},

\(\frac{19,500}{5}\) cm^{3 }= 3,900 cm^{3},

therefore 3,900 cubic centimeters of water will be in the tank when it is \(\frac{3}{5}\) full.

Question 2.

A cube has a surface area of 21 6 square centimeters.

A second cube has edges that are 3 times as long.

How much greater is the surface area of the second cube than the first cube?

Answer:

1,728 cm^{2 }greater is the surface area of the second cube than the first cube,

Explanation:

Given a cube has a surface area of 216 square centimeters as

surface area of cube is 6 X a^{2}= 216 cm^{2},

a^{2 }= 36 cm^{2 }= 6 cm X 6 cm,

edge a = 6 cm,

A second cube has edges that are 3 times long as

6 cm X 3 = 18 cm, Surface area of second cube is 6 x (18)^{2 }=

6 X 18 cm X 18 cm = 1,944 cm^{2}, Now compairing much greater is the

surface area of the second cube than the first cube is 1,944 cm^{2} – 216 cm^{2 }= 1,728 cm^{2}.

**Put on Your Thinking Cap!**

**Problem Solving**

A prism has a square base whose edges each measure 5 centimeters.

The ratio of its height to its width is 4 : 1.

Find the volume of the rectangular prism in cubic centimeters.

Answer:

Given a prism has a square base whose edge each measure 5 centimeters.

height = 4 cm

width = 1 cm

Volume of the rectangular prism = 2l × 2w × 2h

V = 2 × 5 × 2 × 1 × 2 × 4

V = 80 cubic centimeters