Geometry: Rectangular Prism and Pyramid Volume

Podcast

Play an AI-generated podcast conversation about this lesson

Download our mobile app to listen on the go

Get App

Questions and Answers

What is the formula for the volume of a rectangular prism?

$V = ( ext{base area}) imes ( ext{height})$ (correct)
$V = rac{1}{3} ( ext{base area}) imes ( ext{height})$
$V = rac{1}{2} ( ext{base area}) imes ( ext{height})$
$V = ( ext{base length}) imes ( ext{base width}) imes ( ext{height})$

How many edges does a rectangular prism have?

12 (correct)
6
10
8

What is the relationship between the volume of a pyramid and the volume of a prism with the same base and height?

The volume of the pyramid is $rac{1}{3}$ the volume of the prism. (correct)
The volume of the pyramid is twice the volume of the prism.
The volume of the pyramid is $rac{1}{2}$ the volume of the prism.
The volume of the pyramid is equal to the volume of the prism.

A rectangular prism has a volume of 24 $cm^{3}$. What is the volume of the largest pyramid that can be inscribed in the rectangular prism?

8 $cm^{3}$ (C) Signup and view all the answers

A pyramid has a base area of 10 $cm^{2}$ and a height of 6 $cm$. What is the volume of the pyramid?

20 $cm^{3}$ (C) Signup and view all the answers

What is the main purpose of the activity described in the 'EXPLORE' section?

To show that the volume of a pyramid is one-third the volume of a rectangular prism with the same base and height. (B) Signup and view all the answers

Why is it important to use a rectangular prism and a pyramid with equivalent bases and heights in the exploration activity?

To ensure that the pyramid can fit perfectly inside the rectangular prism. (A) Signup and view all the answers

Which of the following is NOT a Learning Target stated for this lesson?

Solve problems involving the volumes of cubes and rectangular prisms. (C) Signup and view all the answers

What are the essential materials needed for the exploration activity described in the 'EXPLORE' section?

A 3D geometrical collapsible pyramid and a rectangular prism. (D) Signup and view all the answers

What concept is being explored inductively in the 'EXPLORE' section of the lesson?

The relationship between the volume of a pyramid and the volume of a rectangular prism. (C) Signup and view all the answers

What is the shape of the base of a right square pyramid?

Square (D) Signup and view all the answers

How many triangular faces does a right square pyramid have?

4 (C) Signup and view all the answers

What is the formula for calculating the volume of a pyramid?

$rac{1}{3} imes (base area) imes (height)$ (A) Signup and view all the answers

A square pyramid has a side length of 6 cm and a height of 9 cm. What is its volume?

108 cm³ (C) Signup and view all the answers

A rectangular prism has the same height and base as a pyramid with a volume of 75 cubic units. What is the volume of the rectangular prism?

150 cubic units (A) Signup and view all the answers

What is the formula for the volume of a pyramid?

$\frac{1}{3} \times$ (base area) $\times$ (height) (D) Signup and view all the answers

In the context of a pyramid, what is the 'slant height'?

The distance from the apex of the pyramid to the midpoint of a side of the base. (A) Signup and view all the answers

How much wood is needed to manufacture 100 paperweights, each with a volume of 16 $in^3$?

1600 $in^3$ (B) Signup and view all the answers

A square pyramid has a base side length of 6 cm and a slant height of 5 cm. What is the height of the pyramid?

4 cm (D) Signup and view all the answers

A suman has a square base with a side length of 2 inches and a height of 3 inches. What is the volume of the suman?

4 $in^3$ (D) Signup and view all the answers

Flashcards

Volume of a Pyramid

The amount of space inside a pyramid, calculated using the formula V = 1/3 * base area * height.

Formula for Volume

The mathematical expression used to calculate the volume of a pyramid: V = 1/3 * B * h, where B is the base area and h is height.