Volume of Solid and Liquid

Find the volume of the cuboid in the image. Length = 7 cm, width = 6 cm, height = 2 cm.

• 64 cm³

• 84 cm³

• 94 cm³

• 104 cm³

Answer explanation

To find the volume of a cuboid, use the formula: Volume = length × width × height. Here, Volume = 7 cm × 6 cm × 2 cm = 84 cm³. Therefore, the correct answer is 84 cm³.

Tags

CCSS.5.MD.C.5B

CCSS.6.G.A.2

Volume 180 cm³. The length of the base is 8 cm and the width is 3 cm. What is the height of the cube?

• 2.5 cm

• 3.5 cm

• 5.5 cm

• 7.5 cm

Answer explanation

To find the height, use the formula for volume: Volume = length × width × height. Rearranging gives height = Volume / (length × width). Substituting values: height = 180 cm³ / (8 cm × 3 cm) = 7.5 cm.

Tags

CCSS.7.G.B.6

The volume of a cuboid is 288 cm³. If the area of the base is 16 cm², what is the height of the cuboid?

• 16 cm

• 18 cm

• 16 cm²

• 18 cm²

Answer explanation

To find the height of the cuboid, use the formula: Volume = Base Area × Height. Rearranging gives Height = Volume / Base Area. Thus, Height = 288 cm³ / 16 cm² = 18 cm. Therefore, the height of the cuboid is 18 cm.

Tags

CCSS.5.MD.C.5B

CCSS.6.G.A.2

A cuboid (shown in the image) has a volume of 1728 cm³, and a base length of 8 cm. What is the area of the blue side?

• 324 cm²

• 324 cm³

• 216 cm²

• 216 cm

Answer explanation

To find the area of the blue side, we first calculate the height using the volume formula: Volume = base length × width × height. Here, 1728 = 8 × width × height. Solving gives height = 27 cm and width = 9 cm. Area = height × width = 27 × 8 = 216 cm².

Tags

CCSS.6.G.A.4

A square has an area of 256 cm². What is the length of its side?

• 16 cm

• 18 cm

• 22 cm

• 24 cm

Answer explanation

To find the side length of a square, take the square root of the area. The area is 256 cm², so the side length is √256 = 16 cm. Therefore, the correct answer is 16 cm.

Tags

CCSS.3.MD.C.7B

CCSS.4.MD.A.3

A cubic tank has a maximum capacity of 1000 ml. What is the length of its sides?

• 100 cm

• 50 cm

• 10 cm

• 5 cm

Answer explanation

To find the length of a side of a cubic tank with a volume of 1000 ml, we use the formula for the volume of a cube: V = side^3. Thus, side = (1000 ml)^(1/3) = 10 cm.

Tags

CCSS.5.MD.C.5B

CCSS.6.G.A.2

A cuboid with a volume of 4900 cm³ has a square face (the shaded side is shown in the image). If its length is 25 cm, find the length of one side of the square face.

• 196 cm

• 121 cm

• 64 cm

• 14 cm

Answer explanation

To find the side of the square face, use the volume formula: Volume = length × width × height. Here, width = height (since it's a square face). Thus, 4900 = 25 × s², leading to s² = 196, so s = 14 cm.

Tags

CCSS.5.MD.C.5B

CCSS.6.G.A.2

A rectangular tank has a square base and a height of 35 cm. The tank is completely filled with water. The tank contains 2,835 liters of water. Find the length of one side of the square base.

• 25 cm

• 18 cm

• 12 cm

• 9 cm

Answer explanation

The volume of the tank is 2835 liters, which is 2835000 cm³. The volume formula for a rectangular tank is V = base_area × height. With height = 35 cm, base_area = 2835000 cm³ / 35 cm = 81000 cm². Since the base is square, side² = 81000, so side = √81000 = 9 cm.

Tags

CCSS.5.MD.C.5B

CCSS.6.G.A.2

• 18 cm

• 24 cm

• 27 cm

• 29 cm

Answer explanation

The volume of water in the cubic container is \(30^3 \times \frac{1}{3} = 9000 \text{ cm}^3\). The rectangular tank has a base area of \(25 \times 20 = 500 \text{ cm}^2\). The height of the water is \(\frac{9000}{500} = 18 \text{ cm}\).

Tags

CCSS.3.MD.A.2

• 6720 ml

• 5040 ml

• 3840 ml

• 2880 ml

Answer explanation

The volume of the tank is 24 cm x 20 cm x 14 cm = 6720 cm³. Since the tank is filled to \frac{3}{4}, the volume of water is \frac{3}{4} \times 6720 = 5040 cm³, which is equivalent to 5040 ml.

Tags

CCSS.5.MD.C.5B

CCSS.6.G.A.2