Question 1:

The corridor is 6 feet wide, 5 feet deep and 8 feet tall. In the corridor, there is a container that is 2 feet wide, 3 feet long and 4 feet tall. How much room is left in the corridor?

Question 2:

John dug soil for 15 rectangular planting pits. Each planting pit is 2 inch long, 4 inch wide and 6 inch deep. What is the volume of the soil removed from each planting pit?

Question 3:

The 2 cisterns were designed as rectangular prisms. Each cistern is 6 m long, 4 m wide and 8 m high. What is the total volume of the 2 cisterns?

Question 4:

Jill bought a portable radio for $19 and 4 sets of headphones for $x each in an electronic shop yesterday. She paid a total of $90. Solve for x.

Question 5:

A box is 4 feet wide, 5 feet deep, and 2 feet high. What is the volume of the box?

Question 6:

In a theater, there were 16 screens, but w screens were closed. Write the expression for the number of screens that were open.

Question 7:

Mandy bought a portable radio for $45 and 4 sets of headphones for $x each in an electronic shop yesterday. She paid a total of $100. Solve for x.

Question 8:

Suzy had 6 crayons in her art set, but she gave away q crayons. Write the expression for the number of crayons in her art set now.

Question 9:

Randy bought 7 packs of balloons for his friend's birthday. Each pack of balloons comes with x balloons. There are 42 balloons in total. Find x.

Question 10:

A box is 2 m long, 2 m wide and 4 m tall. What is the volume of the box?

Question 11:

In a grocery store, there were 7 aisles, but v aisles were closed. Write the expression for the number of aisles that were open.

Question 12:

Andrew bought 9 boxes of shampoo and 4 packs of soap. Each box of shampoo measures 7 cm long, 8 cm wide and 5 cm high. What is the volume of shampoo he bought?

Question 13:

The private swimming pool is 25 ft long, 18 ft wide and 9 ft deep. When Alex filled it with water up to 4 ft deep, what was the volume of the water he used to fill the swimming pool to that depth?

Question 14:

Laura bought 8 packs of balloons for her niece's birthday. Each pack of balloons comes with x balloons. There are 48 balloons in total. Find x.

Question 15:

A television stand is 2.5 feet wide and 8 feet long. It is 4 feet above the floor. What is the volume of space under the television stand?

Question 16:

A box is 2 m long, 2 m wide and 4 m tall. What is the volume of the box?

Question 17:

A basket is 27 cm long, 5 cm wide and 18 cm tall. Inside the basket is a box that is 12 cm long, 1 cm wide and 15 cm tall. How much space is left in the basket?

Question 18:

Mandy sent out invitations to 10 friends for her birthday party. n friends replied and she is waiting for the other 3 friends to reply. Find n.

Question 19:

To entice shoppers, the department store offers special deals. One-way ticket costs y dollars and a round-trip ticket cost $10, which grants purchasers a deal of $4. Find y.

Question 20:

Thomas bought 7 brown woolen scarves for $g each in the department store. He gave a $90 bill to the cashier at the counter. Write the expression for the change he will receive at the counter.

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Answer Keys

Question 1: 216 cubic feet

Question 2: 48

Question 3: 384 cubic meters

Question 4: 17.75

Question 5: 40 cubic feet

Question 6: 16 - w

Question 7: 13.75

Question 8: 6 - q

Question 9: 6

Question 10: 16

Question 11: 7 - v

Question 12: 2520 cm³

Question 13: 1800

Question 14: 6

Question 15: 80

Question 16: 16

Question 17: 2250 cm³

Question 18: 7

Question 19: 8

Question 20: 90 - 7g

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Solutions

Question 1
To find out how much room is left in the corridor, we need to calculate the volume of both the corridor and the container and then subtract the volume of the container from the volume of the corridor. The volume of the corridor can be calculated using the formula: Volume = Length × Width × Height. Plugging in the given measurements, we get: Volume of corridor = 6 feet × 5 feet × 8 feet = 240 cubic feet. Similarly, the volume of the container can be calculated using the same formula: Volume of container = Length × Width × Height. Plugging in the given measurements, we get: Volume of container = 3 feet × 2 feet × 4 feet = 24 cubic feet. To find the room left in the corridor, we subtract the volume of the container from the volume of the corridor: Room left = Volume of corridor - Volume of container = 240 cubic feet - 24 cubic feet = 216 cubic feet. Therefore, there is 216 cubic feet of room left in the corridor.

Question 2
To find the volume of soil removed from each planting pit, we need to multiply the length, width, and depth of the pit. The length of the pit is 2 inches, the width is 4 inches, and the depth is 6 inches. Therefore, the volume of soil removed from each pit is calculated as follows: Volume = length * width * depth = 2 * 4 * 6 = 48 cubic inches.

Question 3
To determine the total volume of the two cisterns, we need to calculate the volume of each cistern and then add them together. Each cistern has a length of 6 m, a width of 4 m, and a height of 8 m. To find the volume of one cistern, we multiply these values: 6 m * 4 m * 8 m = 192 cubic meters. Since there are two cisterns, we multiply the volume of one cistern by 2: 192 cubic meters * 2 = 384 cubic meters. Therefore, the total volume of the two cisterns is 384 cubic meters.

Question 4
Step 1: Write the equation for the total cost: 19 + 4x = 90. Step 2: Simplify the equation by subtracting 19 from both sides: 4x = 71. Step 3: Solve for x by dividing both sides by 4: x = 17.75. Therefore, Jill paid $17.75 for each set of headphones.

Question 5
To find the volume of the box, multiply its width, depth, and height. The formula for the volume of a rectangular prism is V = length * width * height. In this case, the width of the box is 4 feet, the depth is 5 feet, and the height is 2 feet. Therefore, the volume of the box is V = 4 ft * 5 ft * 2 ft = 40 cubic feet.

Question 6
Number of screens that were open = 16 - w

Question 7
Step 1: Write the equation for the total cost: 45 + 4x = 100. Step 2: Simplify the equation by subtracting 45 from both sides: 4x = 55. Step 3: Solve for x by dividing both sides by 4: x = 13.75. Therefore, Mandy paid $13.75 for each set of headphones.

Question 8
6 - q

Question 9
1. Let's represent the number of balloons in each pack by x. 2. Randy bought 7 packs of balloons, so the total number of balloons he has is 7x. 3. We know that there are 42 balloons in total, so we can set up an equation: 7x = 42 4. To solve for x, we need to isolate it on one side of the equation. We can do this by dividing both sides by 7: x = 6. 5. Therefore, each pack of balloons comes with 6 balloons.

Question 10
The volume of the box is calculated by multiplying its length, width, and height. Therefore, the volume of the box is 2 * 2 * 4 = 16 cubic meters.

Question 11
Number of aisles that were open = 7 - v

Question 12
To find the volume of shampoo Andrew bought, we need to calculate the volume of each box and then multiply it by the number of boxes. For each box of shampoo: Length = 7 cm Width = 8 cm Height = 5 cm Volume of each box = Length × Width × Height Volume of each box = 7 cm × 8 cm × 5 cm Volume of each box = 280 cm³ Volume of 9 boxes of shampoo = Volume of each box × 9 Volume of 9 boxes of shampoo = 280 cm³ × 9 Volume of 9 boxes of shampoo = 2520 cm³

Question 13
To find the volume of water used to fill the swimming pool up to 4 ft deep, we need to calculate the volume of a rectangular prism.

The formula for the volume of a rectangular prism is V = l * w * h, where V is the volume, l is the length, w is the width, and h is the height.

In this case, the length (l) of the pool is 25 ft, the width (w) is 18 ft, and the height (h) is 4 ft (since Alex filled the pool up to 4 ft deep).

Substituting these values into the formula, we have:

V = 25 ft * 18 ft * 4 ft

Calculating the multiplication:

V = 450 ft² * 4 ft

V = 1800 ft³

Therefore, the volume of water used to fill the swimming pool up to 4 ft deep is 1800 cubic feet.

Question 14
1. Let's represent the number of balloons in each pack by x. 2. Laura bought 8 packs of balloons, so the total number of balloons she has is 8x. 3. We know that there are 48 balloons in total, so we can set up an equation: 8x = 48 4. To solve for x, we need to isolate it on one side of the equation. We can do this by dividing both sides by 8: x = 6. 5. Therefore, each pack of balloons comes with 6 balloons.

Question 15
The volume of space under the television stand is a rectangular prism. The width, length, and height of the prism are 2.5 feet, 8 feet, and 4 feet, respectively. Therefore, the volume of space under the television stand is 2.5 x 8 x 4 = 80 cubic feet.

Question 16
The volume of the box is calculated by multiplying its length, width, and height. Therefore, the volume of the box is 2 * 2 * 4 = 16 cubic meters.

Question 17
To find the volume of the box, we multiply its length, width, and height: 12 cm × 1 cm × 15 cm = 180 cm³. To find the volume of the basket, we multiply its length, width, and height: 27 cm × 5 cm × 18 cm = 2430 cm³. To find the space left in the basket, we subtract the volume of the box from the volume of the basket: 2430 cm³ − 180 cm³ = 2250 cm³. Therefore, there is 2250 cm³ of space left in the basket.

Question 18
n = number of friends who replied = 7

Question 19
y=8

Question 20
90 - 7g