## Math 8 Chapter 4 Lesson 6: Volume of a vertical prism

## 1. Theoretical Summary

**Formula for volume**

The volume of a vertical prism is equal to the area of the base times the height

\(V = S. h\)

\(S\): bottom area

\(h\): height

## 2. Illustrated exercise

### 2.1. Exercise 1

Observe the vertical prisms in figure 106

Compare the volume of a triangular prism and the volume of a rectangular box.

– Is the volume of a triangular prism equal to the area of the base times the height? Why?

**Solution guide**

– The volume of the triangular prism is half the volume of the rectangular box

– The volume of a triangular prism is equal to the area of the base times the height

Since the volume of the rectangular box is \(5.4.7 = 140\)

\(⇒\) The volume of the triangular prism is \(140 : 2 = 70\)

The area of the base of the triangular prism is: \(\dfrac{1}{2}. 5 .4 = 10\)

The height of the triangular prism is \(7\)

We have: \( 10 .7=70\)

Therefore: The volume of a triangular prism is equal to the area of the base times the height

### 2.2. Exercise 2

The dimensions of a sump are shown in figure 110 (the water surface is rectangular). Calculate how many cubic meters of water the tank can hold when it is full?

**Solution guide**

The swimming pool is divided into two parts: a rectangular box with dimensions \(10m, \;25m,\; 2m\) and a vertical prismatic part with a base of a right triangle with two right angles of \ (2m,\; 7m\) and height \(10m\).

The volume of the rectangular box is:

\(V = 10.25.2 = 500 (m^3) \)

The volume of a triangular prism is:

\(V = Sh = \dfrac{1}{2}. 2.7.10 = 70\) \((m^3) \)

So the number of cubic meters of water in a swimming pool when full is:

\( 500 +70 = 570(m^3) \)

## 3. Practice

### 3.1. Essay exercises

**Question 1:** Find the total area of the vertical prism according to the dimensions given in the figure.

**Verse 2:** The total area of the vertical prism measured by the dimensions shown in the figure is:

**Question 3:** Calculate the volume of the spatial part of a house in the form of a vertical prism according to the dimensions given in the figure.

**Question 4: **Calculate the value of x according to the dimensions given in the figure, knowing the volume of the vertical prism is 15 cm3

### 3.2. Multiple choice exercises

**Question 1: **The volume of the vertical prism according to the dimensions 4cm, 6cm, 10cm is:

A. \(60cm^{2}\)

B. \(90cm^{2}\)

C. \(120cm^{2}\)

D. \(150cm^{2}\)

**Verse 2: **The volume of a vertical prism with dimensions 3cm, 4cm, and 7cm is:

A. 24

B. 42

C. 66

D. 84

**Question 3:** Given a vertical prism ABC.A’B’C’, the base is a right triangle ABC at A with AB=5cm, BC=13cm, AA’=20cm. The area around the correct prism is:

A. \(300cm^{2}\)

B. \(400cm^{2}\)

C. \(480cm^{2}\)

D. \(600cm^{2}\)

**Question 4: **Given a vertical prism ABC.A’B’C’, the base is a right triangle ABC at A with AB=5cm, BC=13cm, AA’=20cm. The volume of the vertical prism is:

A. \(900cm^{3}\)

B. \(1200cm^{3}\)

C. \(1500cm^{3}\)

D. \(600cm^{3}\)

**Question 5: **Given a regular prism ABCD.A’B’C’D’ of volume \(160mm^{2}\), AB=4mm.What is the length of AA’?

A. 12mm

B. 16mm

C. 10mm

D. 20mm

## 4. Conclusion

Through this lesson, you will learn some of the main topics as follows:

- Know the formula for calculating the volume of a vertical prism.
- Know how to apply formulas in calculations.

.

=============

## Leave a Reply