Chapter 1.7, Problem 24PPS

a.

To determine

To find the surface area

Answer to Problem 24PPS

Surface area is40 $fee{t}^2$

Explanation of Solution

Given information:

Length of box=4 feet

Breadth of box= 3 feet

Depth of box= 8 feet

Box filled by sand= $\frac{3}{4}of(depth)$

Formula used:

Surface area= $2(lb+bh+hl)$

Where $l$ is length, $b$ is breadth and $h$ is height.

Calculation:

The box is filled with sand, actual depth is $8-\frac{3}{4}\times (8)$

So, depth is 2 feet

Since there is no lid,

Surface area is $2(lb+bh+hl)-lb$

Substituting values

Surface area= $2(4(3)+3(2)+2(4))-4(3)$

Solving,

Surface area= $2(12+6+8)-12$

So,

Surface area= $2(26)-12$

Hence, surface area is40 $fee{t}^2$

b.

To determine

To find the volume of box

Answer to Problem 24PPS

Volume of the box is 24feet³.

Explanation of Solution

Given information:

Length of box=4 feet

Breadth of box= 3 feet

Depth of box= 8 feet

Box filled by sand= $\frac{3}{4}of(depth)$

Formula used:

Volume= $lbh$

Where $l$ is length, $b$ is breadth and $h$ is height.

Calculation:

The box is filled with sand, actual depth is $8-\frac{3}{4}\times (8)$

So, depth is 2 feet.

Substituting values,

Volume= $(4)(3)(2)$

Solving,

Volume= $(8)\times (3)$

Hence, volume of the box is 24feet³.