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Lesson 7: Volume and surface area word problems

# Volume of triangular prism & cube

Using the formulas for the volume of triangular prism and cube to solve some solid geometry problems. Created by Sal Khan.

## Want to join the conversation?

• So the formula for the volume of solid geometric shapes is the area of one side times the depth/length?
• For prisms and cylinders... yes, Area of Base times Height. For Pyramids and Cones its 1/3 of that.
• What is the formula for the volume of a rectangular pyramid?
• Volume of all types of pyramids = ⅓ Ah, where h is the height and A is the area of the base. This holds for triangular pyramids, rectangular pyramids, pentagonal pyramids, and all other kinds of pyramids.
So, for a rectangular pyramid of length ℓ and width w:
V = ⅓ hwℓ (because the area of the base = wℓ )
• Can you use algebra to find any geometric answers? Ex. Can you use algebra to find the volume of a cube/cone?
• Well, you can't really use algebra to find the volume of anything. The only basic thing to do to find volume is to use the formula for the given shape. What you can use algebra for, is when you want to find the height, radius, or length of a 3-Dimensional shape. For example, to find the radius of a cylinder, you need to know all the other dimensions, such as what pi is defined to (often 3.14) , the height of the shape, and the volume of the shape (the formula for a cylinder is pi times the radius squared times the height). You put the known dimensions into the formula, and then solve for the missing variable, the radius. So you can use algebra in some way in geometry, but only to find a missing height, radius, length, etc. of a 3-Dimensional shape.
• So what is the formula
• Hello!

The formula for finding a triangular prism's volume is the area of the triangle (Width x Height x 1/2) times the depth.

The formula for finding a cube's volume is Base x Height (Length x Width x Height).

I hope this helped! Have a nice day!
• how tofind the volume of a spere
• The volume of a sphere is:
Hope this helps; if you have any questions, feel free to comment.
Have a BLESSED day!
M.L.M.
• 5 x 5
• @ArianahH
The answer to 5 times 5 is 25!
If you have any more questions, feel free to comment below!
Have a BLESSED day!
M.L.M.
• Shouldn't the answer to the 1st problem be 84?
• You've probably already figured it out by now, but for those that have the same question, here is the answer:

The equation for finding the volume of a triangular prism is:
½ × b × h × l = Volume

This means that the equation for the 1st problem would've been:
½ × 7 × 3 × 4 = 42

And you probably just forgot to multiply your equation by ½:
7 × 3 × 4 = 84

If we had a rectangular prism with the same length, width, and height, then yes, the answer would be 84 because we wouldn't have to multiply by ½.