Chapter 12: Q31. (page 480)

The length of a rectangular solid is twice the width, and the height is three times the width. If the volume is 162 cm³, find the total area of the solid.

Short Answer

Expert verified

The total area of the solid is $198 {cm}^{2}$ .

Step by step solution

Step 1. Given information.

The length of the rectangle solid is twice the width and the height is three times the width and the volume is $162 {cm}^{3}$ .

Step 2. Consider the variable.

Let the width of the rectangle is x,

Then, the length of the rectangle solid is2x and the height of rectangle solid is3x .

Step 3. Determine the total area.

Since, the volume of rectangle is $162 {cm}^{3}$ . So,

$\begin{matrix} v = b h \\ 162 = (2 x \times x) (3 x) [substitute] \\ 162 = 6 x^{3} [multiply] \\ x^{3} = 27 [divide] \\ x = 3 [cuberoot] \end{matrix}$

Then, the total surface area is:

$\begin{matrix} T.A. = L.A.+2B \\ = (x + 2 x + x + 2 x) (3 x) +2 (x \times 2 x) [simplify] \\ = 18 x^{2} + 4 x^{2} [multiply] \\ = 22 x^{2} [add] \end{matrix}$

Substitute the value of x.

$\begin{matrix} T.A. = 22 {(3)}^{2} [substitute] \\ = 198 {cm}^{2} [multiply] \end{matrix}$

Thus, the total area is $198 {cm}^{2}$ .

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The length of a rectangular solid is twice the width, and the height is three times the width. If the volume is 162 cm³, find the total area of the solid.

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Consider the variable.

Step 3. Determine the total area.

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The length of a rectangular solid is twice the width, and the height is three times the width. If the volume is 162 cm3, find the total area of the solid.

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Consider the variable.

Step 3. Determine the total area.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Theoretical and Mathematical Physics

Pure Maths

Statistics

Calculus

Applied Mathematics

Study anywhere. Anytime. Across all devices.

The length of a rectangular solid is twice the width, and the height is three times the width. If the volume is 162 cm³, find the total area of the solid.