Chapter A.3, Problem 1E

To determine

To find: The volume and surface area of the given solid cuboid.

Answer to Problem 1E

Solution:

The volume of the solid cuboid is $72\text{cu}\text{in}$ and  the surface area of solid cuboid is $108\text{sq}\text{in}$.

Explanation of Solution

Formula used:

Surface area of the cuboid: The formula to calculate the surface area of cuboid is,

$\text{Surface}\text{area}\text{of}\text{cuboid}=2lh+2lb+2bh$ ….... (1)

Where, l is the length of the cuboid, b is the width of the cuboid and h is the height of the cuboid.

Volume of a cuboid: The formula to calculate the volume of cuboid is,

$\text{Volume}\text{of}\text{Cuboid}=lbh$ …… (2)

Where, l is the length of the cuboid, b is the width of the cuboid and h is the height of the cuboid.

Given:

The length of the given cuboid is $6\text{in}$.

The breadth of the given cuboid is $4\text{in}$.

The height of the given cuboid is $3\text{in}$.

Calculation:

Substitute 6 for l, 4 for b and 3 for h in equation(1), to find the surface area of the cuboid.

$\begin{array}{c}\text{Surface}\text{area}\text{of}\text{cuboid}=2\left(6\right)\left(3\right)+2\left(6\right)\left(4\right)+2\left(3\right)\left(4\right)\\ =36+48+24\\ =108\text{sq}\text{in}\text{.}\end{array}$

The surface area of the cuboid is $108\text{sq}\text{in}\text{.}$

Substitute 6 for l, 4 for b and 3 for h in equation(2), to find the volume of the cuboid.

$\begin{array}{c}\text{Volume}\text{of}\text{Cuboid}=\left(6\right)\left(4\right)\left(3\right)\\ =72\text{cu}\text{in}\text{.}\end{array}$

The volume of the cuboid is $72\text{cu}\text{in}\text{.}$

Final Statement:

Thus, the volume of the cuboid is $72\text{cu}\text{in}\text{.}$ and the surface area of the solid cuboid is $108\text{sq}\text{in}\text{.}$.