Chapter 1.7, Problem 31PPS

a.

To determine

To calculate area.

Answer to Problem 31PPS

Total surface area of the figure=108 $i{n}^2$

Explanation of Solution

Given information:

  

Formula used:

Surface area of rectangle = $l\times b$

Where $b$ is breadth and $l$ is length.

Calculation:

Area of rectangle1,

  =$l\times h$

Height of each layer is 3in so total height of cake is 6in.

Substituting the values,

  =$4\times 6$

Area of rectangle1 = $24i{n}^2$

Area of rectangle2,

  =$b\times h$

Height of each layer is 3in so total height of cake is 6in.

Substituting the values,

  =$3\times 6$

Area of rectangle2 = $18i{n}^2$

Area of rectangle3,

  =$b\times l$

Substituting the values,

  =$4\times 3$

Area of rectangle3 = $12i{n}^2$

Total surface area of the figure=2 $\times$ Area of rectangle1 + Area of rectangle2+ 2 $\times$ Area of rectangle3

(note: there is no frosting on the bottom )

  =$2\times 24+2\times 18+12$

So,

= 48+36+24

Total surface area of the figure=108 $i{n}^2$

b.

To determine

To calculate area.

Answer to Problem 31PPS

Total surface area of the figure=113.04 $i{n}^2$

Explanation of Solution

Given information:

  

Formula used:

Surface area of curved surface= $2\pi rh$

Where r is radius and h is height.

Calculation:

Height of each layer is 4in so total height of cake is 8in.

Surface area of curved surface = $2\pi rh$

  =$2\times 3.14\times 2\times 8$

Surface area of curved surface = 100.48 $i{n}^2$

Surface area of top surface = $\pi r^2$

  =$3.14\times 2\times 2$

Surface area of top surface =12.56 $i{n}^2$

Total surface area of the figure= Surface area of curved surface+ Surface area of top surface

=100.48+12.56

Total surface area of the figure=113.04 $i{n}^2$

To determine

To calculate the total cans used for frosting.

Answer to Problem 31PPS

2.16 cansfor frosting of cuboid cake.

2.26 cans for frosting of cylindrical cake

Explanation of Solution

Given information: c.

  

Total surface area of cuboid cake =108 $i{n}^2$

Total surface area of cylindrical cake=113.04 $i{n}^2$

One can of frosting will cover 50 $i{n}^2$ of cake.

Calculation:

Cans used for frosting of cuboid cake,

  =$\frac{108}{50}$

Therefore,2.16 cans

Cans used for frosting of cylindrical cake,

  =$\frac{113.04}{50}$

Therefore,2.26 cans

d.

To determine

To calculate the radius.

Answer to Problem 31PPS

The radius should be 1.8in

Explanation of Solution

Given information:

Height of each layer is now 5in, new height is 10in.

Surface area for frosting cylindrical cake=113.04 $i{n}^2$

Surface area of curved surface= $2\pi rh$

  $2\pi rh=113.04$

Finding the value of r,

  $r=\frac{113.04}{2\times 3.14\times 10}$

So,

  $r=\frac{113.04}{62.8}$

So,

  $r=1.8$

The radius should be 1.8in