Spectrum Math Grade 7 Chapter 5 Lesson 13 Answer Key Problem Solving

This handy Spectrum Math Grade 7 Answer Key Chapter 5 Lesson 5.13 Problem Solving provides detailed answers for the workbook questions

Spectrum Math Grade 7 Chapter 5 Lesson 5.13 Problem Solving Answers Key

Solve each problem.

Question 1.
On a map, each centimeter represents 45 kilometers. Two towns are 135 kilometers apart. What is the distance between the towns on the map?
The towns are ____ centimeters apart on the map.
Answer:
3

Explanation:
On a map, each centimeter represents 45 kilometers.
Two towns are 135 kilometers apart.
The distance between the towns on the map,
135 ÷ 45 = 3 cm
So, the towns are 3cm centimeters apart on the map.

Question 2.
This hotel lobby is being carpeted. Each unit length represents 1 yard. Carpet costs $22.50 per square yard. How much will it cost to carpet the room?

It will cost _____ to carpet the hotel lobby.
Answer:
$1,383.75

Explanation:
Each unit length represents 1 yard.
Carpet costs $22.50 per square yard.
Total carpet required = 61.5 square yards.
Total cost to carpet the room = 61 x 22.50 = $1,383.75

Question 3.
Hal is going to put tiles down for his patio. Each unit represents 1 square foot. If he wants this shape and tiles cost $3.15 per square foot, how much will Hal end up spending for his patio?

Hal will spend _____ to tile his patio.
Answer:
$189

Explanation:
Each unit represents 1 square foot.
Number of tiles required for the shape = 60
If he wants this shape and tiles cost $3.15 per square foot,
total amount will Hal end up spending for his patio,
60 x 3.15 = $189

Question 4.
A scale drawing shows a room as 10 cm by 7 cm. The scale of the drawing is 2 cm = 5 m. What is the actual area of the room?
The room is ____ square meters.
Answer:
437.5

Explanation:
A scale drawing shows a room as 10 cm by 7 cm.
The scale of the drawing is 2 cm = 5 m.
10 cm = (10 x 5) ÷ 2 = 50 ÷ 2 = 25 m
7 cm = (7 x 5) ÷ 2 = 35 ÷ 2 = 17.5 m
The actual area of the room, 25 x 17.5
So, the room is 437.5 square meters.

Question 5.
A circular rug is 8 feet in diameter. What is its area?
The rug’s area is _____ square feet.
Answer:
50.24

Explanation:
A circular rug is 8 feet in diameter.
Area = πr²
Where π = 3.14
Given,
diameter = 8 feet.
Radius = d/2
r = 8/2
r = 4 feet.
The rug’s area is, 3.14 x 16 = 50.24 square feet.

Solve each problem.

Question 1.
Shawn built a fort in his yard that is 6 feet tall and 6 feet long on all sides. He wants to paint the inside of it (walls, ceiling, and floor). If each bucket of paint will cover 300 square feet, how many buckets of paint should Shawn buy?
Shawn will need to buy ____ bucket of paint.
Answer:
1

Explanation:
Shawn built a fort in his yard that is 6 feet tall and 6 feet long on all sides.
Area = side x side
A = 6 x 6 = 36 square feet.
If each bucket of paint will cover 300 square feet.
Shawn will need to buy one bucket of paint.

Question 2.
Find the surface area of this figure.

The surface area is _____ square meters.
Answer:
51 square meters.

Explanation:

Surface Area = Lateral surface Area + Base Area
The surface area (SA) = (s1 + s2 + s3) L + bh
The surface area (SA) = (5 + 4 + 3) 3  + 5 x 3
SA = 12 x 3 + 15
SA = 36 + 15
SA = 51 square meters.

Question 3.
Rita builds a pool in her backyard. The pool measures 60 feet long, 32 feet wide, and 8 feet deep. How much water will fit in the pool?
_____ cubic feet of water will fit in the pool.
Answer:
15,360 cubic feet.

Explanation:
Rita’s pool measures 60 feet long, 32 feet wide, and 8 feet deep.
V = lbh
V = 60 x 32 x 8
V = 15,360 cubic feet of water will fit in the pool.

Question 4.
Carrie bought a gift that is inside a box that is 3 feet by 2 feet by 3 feet. How much wrapping paper is needed to cover the box?
Carrie needs ____ square feet of wrapping paper.
Answer:
42 square feet.

Explanation:
Carrie bought a gift that is inside a box that is 3 feet by 2 feet by 3 feet.
Given,
Length(l) × width(w) × height(h) of the box = 3feet × 2feet × 3feet.
Wrapping paper needed to cover the box = Surface Area of the cuboid
Wrapping paper needed to cover the box = 2(lw + wh + lh)
= 2(3×2+ 2×3 + 3×3)
= 2(6+6+9) = 2(21)
= 42 square feet
Hence, 42 square feet Wrapping paper is needed to cover the box

Question 5.
The rectangular top of a table is twice as long as it is wide. Its width is 1\(\frac{1}{4}\) meters. What is the area of the tabletop?
The tabletop is ____ square meters.
Answer:
3\(\frac{1}{8}\)

Explanation:
Given,
The rectangular top of a table is twice as long as it is wide.
Its width is 1\(\frac{1}{4}\) meters.
L = 2W
L = 1\(\frac{1}{4}\) = \(\frac{(5 × 2)}{4}\) = \(\frac{5}{2}\)
Now Area, A = LW
A = \(\frac{5}{2}\) x \(\frac{5}{4}\) = \(\frac{25}{8}\) = 3\(\frac{1}{8}\) square meters.

Question 6.
Ian bought enough carpet to cover 500 square feet. He wants to cover a room that is 10 feet 5 inches long by 9 feet 7 inches. About how much will he have left over for the rest of the house?
Ian will have about ____ square feet left over.
Answer:
400

Explanation:
Ian bought enough carpet to cover 500 square feet.
He wants to cover a room that is 10 feet 5 inches long by 9 feet 7 inches.
First, we convert the inches part to feet so that each dimension is in feet only.
To do this, simply divide the inches part by 12 since 1 ft = 12 inches.
10 feet 5 inches = 10\(\frac{5}{12}\) = \(\frac{125}{12}\) ft.
9 feet 7 inches = 9\(\frac{7}{12}\) = \(\frac{115}{12}\) ft.
So, the area of the carpet used for the room is,
\(\frac{125}{12}\) x \(\frac{125}{12}\) = \(\frac{14375}{144}\) ft.
= 99.826 round to nearest tenth as 100 square feet.
​The left over carpet for the rest of the house,
500 − 100 = 400 square feet.

Solve each problem.

Question 1.
A cereal box is shaped like a rectangular prism with a height of 14 in., length of 8 in., and width of 3 in. How much cereal will fit in the box?
_________ cubic inches of cereal will fit in the box?
Answer:
336 cubic inches.

Explanation:
Given box is in the shape of the rectangular prism.
The length is 8 inches.
The width is 3 inches.
The height is 14 inches.
V = l x w x h
V = 8 x 3 x 14
V = 336 cubic inches.
So, the volume of the rectangular prism-shaped box will be 336 cubic inches.

Question 2.
Mr. and Mrs. Hastings are adding a basement to their house. The basement will be 40 feet by 25 feet by 10 feet. How much dirt will have to be removed from under the house to make room for the construction?
______ cubic feet of dirt will have to be removed.
Answer:
10,000 cubic feet.

Explanation:
Mr. and Mrs. Hastings basement will be 40 feet by 25 feet by 10 feet.
Total dirt will have to be removed from under the house to make room for the construction,
40 x 25 x 10 = 10,000 cubic feet.

Question 3.
Jonas is going to have a square cake for his birthday. The cake will be made with two layers that measure 12 inches by 12 inches by 1\(\frac{1}{2}\) inches. How much icing will be needed to cover the cake, including putting icing between the layers?
Jonas will need ____ square inches of icing.
Answer:
432 square inches.

Explanation:
Given that,
Jonas is going to have a square cake for his birthday will be made with two layers that measure 12 inches by 12 inches by 1\(\frac{1}{2}\) inches.
Total icing will be needed to cover the cake, including putting icing between the layers,
Dimensions of one layer: 12 × 12 × 1\(\frac{1}{2}\) inches.
Icing on top of two layers + icing the sides of the cake = 2(12×12) + 4(3×12) = 432 sq in.

Question 4.
The glass for a picture frame that is 10 inches by 12 inches has broken. A new piece of glass costs $0.35 per square inch. How much will a new piece of glass cost?
The glass will cost _________
Answer:
$42.00

Explanation:
Given that,
The glass for a picture frame that is 10 inches by 12 inches has broken.
10 x 12 = 120 inches.
A new piece of glass costs $0.35 per square inch.
Total cost of a new piece of glass = 120 x 0.35 = $42.00

Question 5.
An Olympic-size swimming pool measures 50 meters by 15 meters. What size pool cover will be needed to cover the pool for the winter?
A pool cover that is _____ square meters will be needed.
Answer:
750 square meters.

Explanation:
Given that,
An Olympic-size swimming pool measures 50 meters by 15 meters.
Total size pool cover will be needed to cover the pool for the winter,
50 x 15 = 75 sq mts.

Question 6.
Ebony built a model of an Egyptian pyramid. Her model measures 0.5 meters along the bottom of one side and 0.3 meters tall. What is the volume of her pyramid?
Ebony’s pyramid has a volume of _____ cubic meters.
Answer:
0.025 cubic meters.

Explanation:
Given that,
Ebony model measures 0.5 meters along the bottom of one side and 0.3 meters tall.
The volume pyramid = \(\frac{1}{3}\) (l x w x h)
V = \(\frac{1}{3}\) (0.5 x 0.5 x 0.3)
V = \(\frac{0.075}{3}\)
V = 0.025 cubic meters.