Using the volume formula V = l × w × h, we have 240 = 8 × 6 × h. This gives us 240 = 48h, so h = 240 ÷ 48 = 5 inches. Choice B results from incorrectly dividing by the full volume instead of the base area. Choice C comes from dividing 240 by 24 instead of 48. Choice D is the base area, not the height.

When you encounter volume problems with rectangular prisms, remember that volume equals length × width × height ($$V = l \times w \times h$$). You're given the volume and two dimensions, so you need to work backwards to find the missing dimension.

Start with the volume formula: $$V = l \times w \times h$$. Substituting the known values: $$360 = 9 \times w \times 5$$. Simplify the right side: $$360 = 45w$$. To solve for width, divide both sides by 45: $$w = 360 ÷ 45 = 8$$ units.

Let's check why each answer choice is right or wrong. Choice A ($$8$$ units) is correct because $$9 \times 8 \times 5 = 360$$ cubic units. Choice B ($$6$$ units) would give you $$9 \times 6 \times 5 = 270$$ cubic units, which is too small. Choice C ($$72$$ units) represents a common error where students multiply length and height ($$9 \times 5 = 45$$) instead of dividing the volume by this product. This gives $$9 \times 72 \times 5 = 3,240$$ cubic units, which is way too large. Choice D ($$45$$ units) is the result of multiplying length and height rather than using it as a divisor, giving $$9 \times 45 \times 5 = 2,025$$ cubic units.

Remember this strategy: when finding a missing dimension in volume problems, multiply the two known dimensions first, then divide the total volume by that product. This prevents calculation errors and keeps your work organized.

The base area of the pool is 20 × 12 = 240 square feet. With 1200 cubic feet of water: 1200 = 240 × h, so h = 1200 ÷ 240 = 5 feet. Choice A comes from incorrectly assuming the depth is proportional to half the volume ratio. Choice B uses the wrong calculation method. Choice D results from adding instead of using the volume formula correctly.

Original volume: V = 12 × 8 × 6 = 576 cubic inches. For the new boxes: 576 = 9 × 8 × h, so 576 = 72h, and h = 576 ÷ 72 = 8 inches. Choice A is the original height. Choice C is the new length. Choice D is the original length. Students often confuse these dimensions when working with multiple boxes.

The core skill is using volume formulas to find the volume of a rectangular prism. The length, width, and height represent the perpendicular sizes, with length and width basing the rectangle and height extending it. The formula connects to stacking cube layers, each base-filled with length × width cubes, for height layers total. Volume is base area × height, reflecting packed cubes. A misconception is reporting volume in square units, but it must be cubic for 3D. Formulas are efficient for rapid problem-solving without cubes. This versatility fits items like shoeboxes, with volume 11 × 6 × 3 = 198 cubic inches, answer C.

When you encounter problems involving boxes or containers with the same volume, you're working with the formula for volume of a rectangular prism: Volume = length × width × height. Since both boxes have equal volumes, you can set up an equation to find the missing dimension.

First, calculate Box A's volume: $$6 \times 4 \times 9 = 216$$ cubic inches. Since Box B has the same volume, you know that $$8 \times 6 \times \text{height} = 216$$ cubic inches.

To find Box B's height, divide the total volume by the known dimensions: $$216 ÷ (8 \times 6) = 216 ÷ 48 = 4.5$$ inches. You can verify this: $$8 \times 6 \times 4.5 = 216$$ cubic inches, which matches Box A's volume.

Looking at the wrong answers: Choice A ($$3$$ inches) would give Box B a volume of only $$144$$ cubic inches, which is too small. Choice B ($$9$$ inches) might tempt you because it's Box A's height, but this would make Box B's volume $$432$$ cubic inches—twice as large as needed. Choice C ($$6$$ inches) uses Box B's width, creating a volume of $$288$$ cubic inches, which is also too large.

Remember this strategy: when two 3D shapes have equal volumes, set up the equation Volume₁ = Volume₂, then solve for the unknown dimension. Always double-check by calculating the final volume to ensure it matches the given volume.

When you encounter problems about pouring water from one container to another, you're working with volume - the amount of space the water takes up. The key insight is that water keeps the same volume no matter what container it's in.

First, find the volume of water in the original container. Volume of a rectangular container equals length × width × height: $$15 \text{ cm} × 10 \text{ cm} × 8 \text{ cm} = 1,200 \text{ cubic cm}$$. This is how much water Jamie has.

When she pours this water into the new container, the volume stays exactly the same: $$1,200 \text{ cubic cm}$$. Now you need to find how high this volume will reach in the new container. You know the new container's length ($$12$$ cm) and width ($$10$$ cm), so: $$12 \text{ cm} × 10 \text{ cm} × \text{height} = 1,200 \text{ cubic cm}$$. Solving for height: $$120 × \text{height} = 1,200$$, so $$\text{height} = 10 \text{ cm}$$.

Looking at the wrong answers: Choice A ($$8$$ cm) incorrectly assumes the water height stays the same as in the original container. Choice B ($$12$$ cm) mistakenly uses the new container's length as the height. Choice D ($$15$$ cm) incorrectly uses the original container's length.

Remember this pattern: when liquid moves between containers, calculate the volume first, then use that volume with the new container's dimensions to find the unknown measurement. Volume always stays constant when you pour from one container to another.

First, find the original volume: V = b × h = 18 × 3 = 54 cubic feet. For the new aquarium with the same volume: 54 = b × 2, so b = 54 ÷ 2 = 27 square feet. Choice A comes from incorrectly subtracting the height difference from the base area. Choice C results from doubling the original base area. Choice D is the total volume, not the base area.

When you encounter a volume problem involving a rectangular prism (like this planter), remember that volume equals length × width × height. You know the total volume and two dimensions, so you need to find the third dimension.

Start with the volume formula: Volume = length × width × height. You're given that the volume is $$480$$ cubic centimeters and the base is $$12$$ cm by $$8$$ cm. First, calculate the area of the base: $$12 \times 8 = 96$$ square centimeters.

Now you can find the depth (height) by dividing the total volume by the base area: $$480 ÷ 96 = 5$$ centimeters. This means the planter is $$5$$ cm deep.

Looking at the wrong answers: Choice A ($$4$$ cm) would give you a volume of only $$12 \times 8 \times 4 = 384$$ cubic centimeters, which is too small. Choice B ($$96$$ cm) is a trap—this is actually the base area, not the depth. If the depth were $$96$$ cm, the volume would be $$12 \times 8 \times 96 = 9,216$$ cubic centimeters, which is way too large. Choice C ($$6$$ cm) would create a volume of $$12 \times 8 \times 6 = 576$$ cubic centimeters, which exceeds the given volume.

The correct answer is D ($$5$$ cm).

Remember this strategy: when you know volume and two dimensions of a rectangular prism, find the area of the known face first, then divide the volume by that area to find the missing dimension.

Volume formulas are used to find the volume of a rectangular prism by quantifying its internal capacity in cubic units. The dimensions represent length as 9 units along one base side, width as 2 units along the other, and height as 5 units upward. This connects to cube layers since each layer holds as many cubes as the base area, with height determining the layer count. The base area of 9 × 2 is multiplied by height 5 to compute the total volume effectively. A misconception is adding dimensions instead of multiplying, which doesn't account for the space filled. These formulas are efficient for rapid results in real-world applications like storage. They generalize across shapes, simplifying volume problems in math and beyond.