Volume of Prisms 04:28 minutes

Video Transcript

Transcript Volume of Prisms

Call now to receive your shipment of premium, evil piranhas! But wait, if you order within the next 3 minutes, you'll receive the best discount ever! Don't miss this amazing deal-of-a-lifetime! Dr. Evil was so convinced by the infomercial that he absolutely had to add some piranhas to his evil caché of animals. The only problem is that he needs to purchase an evil fish tank before they are delivered, so he decides to check out the local, evil pet shop. But in order to figure out the correct size, he needs to calculate the Volume of Prisms. Since he ordered 8 piranhas and since each piranha needs at least 3,000 cubic inches of water to remain evil, he'll need a tank with a volume of at least 24,000 cubic inches to ensure that the piranhas have enough evil space to swim around evily. There are so many evil aquariums to choose from, but which is the most evil? First, he sees an aquarium that's a triangular prism, which is a prism with a triangle as its base. Unfortunately, the total volume isn't listed in the store. So, let's help Dr. Evil figure out the volume of the tanks. From the info tag, we can see that the triangular base has an area of 450 square inches and that the height of the tank is 40 inches. How can we use this information to help Dr. Evil calculate the volume of this tank? The volume of any prism is the area of its base times its height. By substituting in the values for the area of the base and the height, the volume of this triangular prism comes out to be 18,000 cubic inches. Unfortunately, that's too small for all the evil fish Dr. Evil wants. Besides, Dr. Evil doesn't want to be evil to his evil fish. Next, Dr. Evil takes a look at the classic evil aquarium, shaped like a rectangular prism. It's called a rectangular prism because the base of the tank is a rectangle. We can see that the info tag says that the width of the tank is 48 inches, the depth is 21 inches, and the height is 35 inches. In order to use the same formula – the volume of the prism equals the area of the base times the height – we need to help Dr. Evil figure out the area of the base. We just don't know the area of the rectangle yet, but if you remember, the formula for the area of a rectangle is simply the product of its two sides. In the case of this evil aquarium, the area of the base can be found by multiplying the width by the depth. This leaves us with the formula for the volume: width times depth times height. Substituting in the values gives us a volume of 35,280 cubic inches. Great! That's plenty evil enough! All of his new piranhas will have enough space for their evil fishy doings. Let's review. When calculating the volume of a prism, you just need to know two things: the area of the base and the height. Then, to get the volume, you simply multiply those two together. Be sure to check the units before you multiply! You don't want to multiply feet times meters! That would be evil! Additionally, the shape of the base doesn't matter, the formula always works. The volume of a prism equals the area of the base times the height, or 'v' equals 'b' times 'h'. Now, he's back at home and his evil fish tank is all set up. A delivery comes and he eeeeevily opens the box. Toy fish? That's not what he ordered... or is it? Remember, always be sure to read the EVIL fine print!