Volume Of A Prism - Varsity Tutors

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Volume of a Prism

Study Guide

Key Definition

The volume $V$ of a prism is calculated as the area of the base $B$ times the height $h$, or $V = B \times h$.

Important Notes

• •The base $B$ can be any polygon.
• •Ensure all measurements are in the same units before calculating.
• •Volume is measured in cubic units, such as $cm^3$.
• •Use the formula $A = l \times w$ to find the area of a rectangular base.
• •Common units for volume include $m^3$, $ft^3$, and $in^3$.

Mathematical Notation

$\times$ represents multiplication$\div$ represents division$cm^3$ denotes cubic centimeters$B$ is the base area$h$ is the heightRemember to use proper notation when solving problems

Why It Works

The formula $V = B \times h$ works because it multiplies the area of the base by the height, filling the entire volume of the prism with cubes of the base area.

Remember

Always calculate the base area first, then multiply by height: $V = B \times h$.

Quick Reference

Volume Formula:$V = B \times h$

Understanding Volume of a Prism

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Beginner Explanation

A prism is a solid three-dimensional shape with two parallel, identical bases and flat faces connecting them. To find its volume, first calculate the area of the base (B). Then multiply by the height (h) of the prism. The formula is $V = B \times h$. For example, if a rectangular base has length 5 cm and width 3 cm, then $B = 5 \times 3 = 15\ cm^2$; if the height is 4 cm, then $V = 15 \times 4 = 60\ cm^3$.Now showing Beginner level explanation.

Practice Problems

Test your understanding with practice problems

1

Quick Quiz

Single Choice QuizBeginner

What is the volume of a prism with a base area of $20\ cm^2$ and a height of $10\ cm$?

A$200\ cm^3$B$100\ cm^3$C$150\ cm^3$D$250\ cm^3$Check AnswerPlease select an answer for all 1 questions before checking your answers. 1 question remaining.2

Real-World Problem

Question ExerciseIntermediate

Teenager Scenario

Imagine you have a box with a base area of $30\ cm^2$ and height $15\ cm$. How much space does it occupy?Show AnswerClick to reveal the detailed solution for this question exercise.3

Thinking Challenge

Thinking ExerciseIntermediate

Think About This

If the base area of a prism is doubled, how does that affect the volume?

Show AnswerClick to reveal the detailed explanation for this thinking exercise.4

Challenge Quiz

Single Choice QuizAdvanced

A prism has a triangular base with area $35\ cm^2$ and a height of $12\ cm$. What is the volume?

A$420\ cm^3$B$360\ cm^3$C$480\ cm^3$D$400\ cm^3$Check AnswerPlease select an answer for all 1 questions before checking your answers. 1 question remaining.

Recap

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