Chapter ISG, Problem 1.5.4P

a.

To determine

To find area of faces

Answer to Problem 1.5.4P

Area of face₁ is 111.38 in²

Area of face₂is 35.81 in²

Area of face₃ is 75.27 in²

Explanation of Solution

Given information:

Length=15.3 in

Breadth=7.28 in

Height=4.92 in

Formula used:

Area of rectangle= $length\times breadth$

Calculation:

Area of face₁,

Substituting values,

Area= $15.3\times 7.28$

Solving,

Area=111.38 in²

Hence, area of face₁ is 111.38 in²

Area of face₂,

Substituting values,

Area= $7.28\times 4.92$

Solving,

Area=35.81 in²

Hence, area of face₂is 35.81 in²

Area of face₃,

Substituting values,

Area= $4.92\times 15.3$

Solving,

Area=75.27 in²

Hence, area of face₃ is 75.27 in²

b.

To determine

To find surface area of box

Answer to Problem 1.5.4P

Surface area of box is 444.92 in²

Explanation of Solution

Given information:

Length=15.3 in

Breadth=7.28 in

Height=4.92 in

Formula used:

Surface area of cuboid= $2(length\times breadth+breadth\times height+height\times length)$

Calculation:

Here, surface area of the box is

2(sum of area of the faces)

Substituting values,

Surface area= $2(111.38+35.81+75.27)$

Solving,

Surface area=2(222.46)

Hence, surface area of box is 444.92 in²

c.

To determine

To find range of values

Answer to Problem 1.5.4P

Range is 10.38

Explanation of Solution

Given information:

Length=15.3 in

Breadth=7.28 in

Height=4.92 in

Formula used:

Range is,

  $range=\max -\min$

Calculation:

The maximum length is 15.3 in

The minimum length is 4.92 in

For range, substituting the value,

  $range=15.3-4.92$

On solving,

  $range=10.38$

Hence, range is 10.38

d.

To determine

To find the surface area

Answer to Problem 1.5.4P

Surface area is 438.2 in²

Explanation of Solution

Given information:

Length=15.1 in

Breadth=7.28 in

Height=4.92 in

Formula used:

Surface area of cuboid= $2(length\times breadth+breadth\times height+height\times length)$

Calculation:

Substituting values,

Surface area= $2(15.1\times 7.28+7.28\times 4.92+4.92\times 15.1)$

Solving,

Surface area= $2(109.9+35.81+74.29)$

So,

Surface area= $2(219.10)$

Hence, surface area is 438.2 in²

e.

To determine

To explain a statement.

Answer to Problem 1.5.4P

The explanation is as follows

Explanation of Solution

Given information:

Surface areas of box

Calculation:

Surface area of box is 444.92 in²with no error and surface area is 438.2 in².

A little error can result too much greater difference in surface area as it deals with squares which can have greater values.