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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 is198cm2 .

Step by step solution

01

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 162cm3.

02

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 .

03

Step 3. Determine the total area.

Since, the volume of rectangle is162cm3 . So,

v=bh162=(2x脳x)(3x)[substitute]162=6x3[multiply]x3=27[divide]x=3[cuberoot]

Then, the total surface area is:

T.A.=L.A.+2B=(x+2x+x+2x)(3x)+2(x脳2x)[simplify]=18x2+4x2[multiply]=22x2[add]

Substitute the value of x.

T.A.=22(3)2[substitute]=198cm2[multiply]

Thus, the total area is198cm2 .

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