Q&A for How to Find The Height Of a Prism

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How do I find the height of a cylinder given the volume?

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You can use Method 1 and the formula V = Ah. The base of a cylinder is a circle, so A will equal the area of the circle, which is pi x r^2. As long as you know the radius of the circle, you should be able to solve for h.

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How can I find the height of a rectangular prism with the width, length and area of base?

Donagan

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You also need to know the volume, in which case, you would divide the volume by the area.

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How do I find the width of a rectangular prism?

Donagan

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Assuming you know the volume, divide the volume by the height, then divide by the length.

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A rectangular box has a volume of 2860 cubic m. What could be the dimension of its rectangular base if its height is 40 cm?

Donagan

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Divide the volume by the height. That gives you the area of the rectangle. Divide the area by any convenient number. The quotient is one possible dimension of the rectangle. The other possible dimension is the "convenient number" you chose.

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How do I find the height if I know the volume and area?

Donagan

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Divide volume by area.

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How to find the length of a prism?

Donagan

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If you mean the length of the base of a prism, you must first have other information such as the height, width, base area, surface area, or volume of the prism.

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How are you supposed to find the height of a triangular prism if you need the volume? There's no way to find the volume without knowing the height.

Community Answer

You can't solve for volume and for height, you can only solve for one unknown variable. However, if you know the surface area and the side lengths of the base, you can find the height without the volume, as described in Method 4.

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How do I find the length when I already have the height, width and volume?

Donagan

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Multiply the height by the width, then divide that number into the volume.

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What's the volume of a square prism of base 4 cm per side and 4 cm height?

Donagan

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Given a prism with a height of 4 cm and a square base 4 cm on a side, this prism is a cube. Its volume is 4 x 4 x 4 = 64 cubic centimeters.

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I'm confused when trying to figure out how to find the height of a triangle with volume; you said we needed to use the height to find the volume? We already know the volume and are trying to find height.

Donagan

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The formula for the volume of a pyramid is V = (bh) / 3, where b is the area of the base, and h is the pyramid's height. Re-work the equation to solve for h: h = 3V / b. So the height is three times the volume, divided by the base's area.

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How can I find the height of a rectangular prism without the volume and surface area but given the length and width?

Donagan

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You don't have enough information to find the height.

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How do I find the radius of a cylinder?

Donagan

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Assuming you know the volume, divide the volume by the height, then divide by pi, then find the square root.

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How can I find the height of a cylinder given its surface area?

Donagan

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You would need other information, too, such as the radius or circumference. Dividing the circumference into the surface area gives the height.

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How do I find dimensions of triangular prisms if given the volume?

Donagan

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A triangular prism has three dimensions. If you know the volume, you must also know two of the dimensions in order to find the third. If you know fewer than two of the dimensions, you cannot find the other dimension(s).

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If I only have the length and width of a rectangular prism (ex: 5,2), then how would I find V? Would that be possible?

Donagan

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No, not without the height.

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Question

How do I find the height of a pyramid?

Donagan

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The formula for the volume of a pyramid is one-third the base area multiplied by the height. So you have to know the volume, multiply it by 3, and divide that product by the base area in order to find the height.

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