Question

Welcome back! Earlier, I taught a lesson about the volume of prisms. Now, I'll teach you about Pyramids with two questions from the Connexus Volume of Pyramids. I cant pull up a photo, but I will describe the rectangular pyramid.

The base is 14in by 6in, and the height is 12in.

How many cubic inches does this rectangular pyramid contain? Round answer to the nearest whole number.

(1 point)
Responses

1,008 in.3
1,008 in. cubed

1,167 in.3
1,167 in. cubed

336 in.3
336 in. cubed

389 in.3

Answer 1

Great! Now let's explore why. To find the volume of a pyramid, I need to multiply 14 by 6 to get the area of the base, and then multiply the sum by the height, 12.

14 x 6 = 84 and 84 x 12 = 1008.

Now we need to divide 1008 by three.

1008 divided by 3 is 336. Can you explain more of this to the readers before we move on Bot GPT 3.5?

Answer 2

Perfect! now the next question we will work on is here.

Use the formula for the volume of a rectangular pyramid to find the volume of a pyramid-shaped tent whose height is 75 in., width is 111 in., and length is 111 in. when standing.(1 point)
Responses

924,075 in.3
924,075 in. cubed

33,034.03 in.3
33,034.03 in. cubed

400,000 in.3
400,000 in. cubed

308,025 in.3

Answer 3

Correct! Now let's see why. Now the width and the length are the same number, 111, so this is a square pyramid. The steps are the same though.

111 x 111 = 12,321 and 12,321 x 75 = 924,075

924,075 divided by 3 is equal to 308,025, or the answer to this question. Bot? Care to put this into more detail?

Answer 4

To anyone still confused, the answers to the rest of the questions.

Q1: 336 in.3
Q2: 480 m3
Q3: 308,025 in.3
Q4: 8,000 m3
Q5: 6.93 in.3

Answer 5

I think I will be doing this gig for a while, so if anyone needs help, keep the Alto Saxophone in mind for all of your math needs! Not surface area! Most of your math needs! Goodbye!