Chapter 12: Q6. (page 478)

Refer to rectangular solids with dimensions l, w and h. Complete the following table.
$\begin{matrix} l & 9 \\ w \\ h & 2 \\ L.A. & 60 \\ T.A. \\ V \end{matrix}$

Short Answer

Expert verified

$\begin{matrix} l & 9 \\ w & 6 \\ h & 2 \\ L.A. & 60 \\ T.A. & 168 \\ V & 108 \end{matrix}$

Step by step solution

Step 1. Given information.

The length and height of a rectangle are 9 and 2 respectively. And the lateral area is 60.

Step 2. Write the concept.

The lateral area of the rectangle is given by:

$L.A. = Perimeter \times Height$

The total area of the rectangle is given by:

$T.A. = L.A.+ 2 (Base)$

The volume of rectangle is given by:

$V = l \times w \times h$

Step 3. Determine the value.

Firstly, find the third dimension of the rectangle using the lateral area.

$\begin{matrix} L.A. = 2 (l + w) \times h \\ 60 = 2 (9 + w) \times 2 \\ \frac{60}{2} = (18 + 2 w) \\ 30 = 18 + 2 w \end{matrix}$

Then,

$\begin{matrix} 30 - 18 = 2 w \\ w = \frac{12}{2} \\ = 6 unit \end{matrix}$

Now,

$\begin{matrix} T.A. = 60 + 2 (9 \times 6) \\ = 60 + 2 (54) \\ = 60 +108 \\ = 168 {unit}^{2} \end{matrix}$

And the volume is:

$\begin{matrix} V = l \times w \times h \\ = 9 \times 6 \times 2 \\ = 54 \times 2 \\ = 108 {unit}^{3} \end{matrix}$

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Refer to rectangular solids with dimensions l, w and h. Complete the following table.
$\begin{matrix} l & 9 \\ w \\ h & 2 \\ L.A. & 60 \\ T.A. \\ V \end{matrix}$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Write the concept.

Step 3. Determine the value.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Pure Maths

Decision Maths

Calculus

Statistics

Applied Mathematics

Study anywhere. Anytime. Across all devices.

Refer to rectangular solids with dimensions l, w and h. Complete the following table.l9wh2L.A.60T.A.V

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Write the concept.

Step 3. Determine the value.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Pure Maths

Decision Maths

Calculus

Statistics

Applied Mathematics

Study anywhere. Anytime. Across all devices.

Refer to rectangular solids with dimensions l, w and h. Complete the following table.
$\begin{matrix} l & 9 \\ w \\ h & 2 \\ L.A. & 60 \\ T.A. \\ V \end{matrix}$