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How do you find the volume of a box?

Grace Imson, MA
Math Instructor, City College of San Francisco
Grace Imson is a math teacher with over 40 years of teaching experience. Grace is currently a math instructor at the City College of San Francisco and was previously in the Math Department at Saint Louis University. She has taught math at the elementary, middle, high school, and college levels. She has an MA in Education, specializing in Administration and Supervision from Saint Louis University.

Grace Imson, MA

Math Instructor, City College of San Francisco

Expert Answer

The volume of a box is equal to the product of the three dimensions of the box. You would multiply the length, the width, and the height of the box to find its volume. Make sure the dimensions have the same unit. Some tricky questions give different units for each dimension.

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Question

How would you find the volume of a water tank?

Grace Imson, MA
Math Instructor, City College of San Francisco
Grace Imson is a math teacher with over 40 years of teaching experience. Grace is currently a math instructor at the City College of San Francisco and was previously in the Math Department at Saint Louis University. She has taught math at the elementary, middle, high school, and college levels. She has an MA in Education, specializing in Administration and Supervision from Saint Louis University.

Grace Imson, MA

Math Instructor, City College of San Francisco

Expert Answer

Assuming the tank is a cylinder, you'll need the radius or diameter of one of the circular bases as well as the height of the tank. Calculate the area of the circle using πr² (if you have the diameter, divide it in half to get the radius). Then, just multiply the area of the circular base by the height of the tank to find its volume.

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Question

How do I calculate the volume of compound shapes?

Community Answer

If the compound shapes are made up of basic geometric solids, then you can try dissecting them into their simpler parts. Their volumes will be additive.

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Question

Are there alternate methods for calculating volume?

Community Answer

Yes -- you could divide the mass of the object by the density (assuming you know both).

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Question

How do I calculate the volume of a 6-sided cube with different base and top areas?

Donagan

Top Answerer

In the case of a cube, the base area is always equal to the top area.

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Question

What method lets us derermine the volume of an oddly shaped object?

Donagan

Top Answerer

Measure the object's water displacement.

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How do I calculate the volume of a triangular prism?

Community Answer

Calculate the area of the base (the triangle) and multiply by the height (the dimension that is not part of the triangle).

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Question

What is the diameter of the base of the cylinder if the volume of the cylinder is 81 pi cm3?

Community Answer

Volume = base area * height = diameter*pi/4*height. Diameter = 4*volume/(pi*height). You can't find the base diameter without knowing the height.

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Question

Can I calculate the volume of a box by observing the speed at which it fills with water?

Community Answer

You would need to know the flowrate of the incoming water. Example: if you know that a pipe carrying 1l/s of water fills the box in 10 seconds, your box is 10l big.

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Question

Is there a formula that works for all shapes?

Donagan

Top Answerer

No.

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Question

If I have the volume of 250 gallons and the diameter of the cylinder, how would I calculate the unknown height? I can't remember how to solve for the unknown from your equation of V = Pi x r(squared) x h.

Donagan

Top Answerer

Convert gallons to cubic feet (0.1337 cubic foot in a US gallon, and .16 cubic foot in an Imperial gallon). Find the cross-sectional area of the cylinder by finding the radius (half the diameter), squaring it and multiplying by pi. Then divide the volume you calculated by the area you calculated. That gives you the height of the cylinder.

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Question

If one makes a sizable dent in a gallon bucket, does it still hold a gallon?

Donagan

Top Answerer

It's not likely.

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Question

How can I find the volume of a triangular-based pyramid?

Donagan

Top Answerer

It's one-third of the area of the triangular base multiplied by the height of the pyramid.

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Question

Does this apply to triangular hexagonal and others or just square pyramid?

Community Answer

If you know the area of the base, you can use the same formula for any pyramid or cone. The shape of the base doesn't matter if you know its area.

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Question

If we have the area of a room, how we calculate its volume?

Donagan

Top Answerer

Multiply the area by the height of the room.

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Question

How much concrete do I need to cover a space 18' x 10' if the concrete is 3" thick?

Donagan

Top Answerer

Multiply 18 x 10 x ¼ to get the volume in cubic feet.

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Question

How can I calculate the volume of a boulder?

Donagan

Top Answerer

The best you could do is to measure the boulder in three directions and then multiply the three dimensions together to get an estimate of the volume.

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How do I calculate volume of an irregular object?

Donagan

Top Answerer

See Calculate the Volume of an Irregular Object .

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Question

How do I calculate the volume of a cuboid?

Donagan

Top Answerer

The volume of a cube is the cube of the length of any edge -- that is, an edge multiplied by itself and then multiplied by itself again.

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Question

How do I calculate volume of a tube coil?

Donagan

Top Answerer

If you're interested in the volume inside the tube (not including the tube's walls), measure the inside diameter of the tube, divide it in half, square that number, multiply by pi, then multiply by the full length of the tube (measured carefully in the coiled shape or when it's straightened out).

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Question

What is the formula of finding the volume of a sphere?

Donagan

Top Answerer

Volume = (4/3)(πr³), where r is the radius.

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How do I find the volume of a 3D half-circle?

Donagan

Top Answerer

If you're asking about a hemisphere, take half the volume of the full sphere. The formula for the volume of a full sphere is 4/3(πr³), where π is 3.14, and r is the radius of the sphere.

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How do I find the height of a cube if the volume is 27 cubic meters?

Donagan

Top Answerer

The height of a cube is the cube root of its volume. In this case it's 3 meters.

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Question

It's really complicated to the formula of a sphere, any help?

Donagan

Top Answerer

Well, let's un-complicate it. The volume of a sphere is (4/3)(π)(r³). So first you multiply 4 by 3.14: that's 12.56. Then divide by 3: that's 4.186. Then multiply by the sphere's radius three separate times. You're done. Here's an example: the volume of a sphere with a radius of 5 units is 4.186 multiplied by (5x5x5). That's (4.186)(125) = 523.25 cubic units.

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What if area and thickness are given, why do we multiply the two together to get volume?

Donagan

Top Answerer

You're transitioning from two-dimensional area to three-dimensional volume. Think of it as stacking a bunch of very thin areas on top of each other to form the volume. The thickness tells us how many areas we stack to form the volume.

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Question

How would I calculate the volume of a piece of PVC pipe when I'm given only the mass, density, and the inner and outer diameters?

Donagan

Top Answerer

Divide the mass by the density. (Because you're not given the length of the pipe, you don't need the diameters.)

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How do you find volume of a hollow cylinder?

Donagan

Top Answerer

Volume = πr²h, where r is the cylinder's radius and h is its height (or length).

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Question

Can depth be seen or multiplied in the same manner that height is multiplied or seen?

Donagan

Top Answerer

Yes, if you're talking about a prism, a cylinder or a container of some sort, "depth" and "height" usually refer to the same thing.

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What is the height of the container if the volume is 706in^3 and the radius 5 inches?

Donagan

Top Answerer

Assuming the container is a cylinder, you would first find the base area (πr² = 25π = 78.54 square inches) and then divide that into the volume.

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How would I calculate the volume of a syringe?

Donagan

Top Answerer

Presumably the syringe is cylindrical. In that case, the volume is πr²h, where r is the inside radius and h is the length of the syringe's interior.

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