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  3. ZuAI AP College Board Maths 2020
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Volumes with Cross Sections

Sarah Miller

Sarah Miller

5 min read

Next Topic - Squares as Cross Sections
Study Guide Overview

This study guide covers calculating volumes of solids with known cross-sectional areas using definite integrals. It explains the key concepts, provides a step-by-step approach, and offers worked examples and practice questions. The guide also includes a glossary and emphasizes the importance of the cross-sectional area function, integral setup, and correct units.

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Previous Topic - Multiple AreasNext Topic - Squares as Cross Sections

Question 1 of 12

Alright, let's start with an easy one! 🚀 If the cross-sectional area of a solid is given by A(x)=2xA(x) = 2xA(x)=2x and we want to find the volume between x=0x = 0x=0 and x=1x = 1x=1, which integral should we evaluate?

∫012x,dx\int_{0}^{1} 2x , dx∫01​2x,dx

∫01x2,dx\int_{0}^{1} x^2 , dx∫01​x2,dx

∫012,dx\int_{0}^{1} 2 , dx∫01​2,dx

∫022x,dx\int_{0}^{2} 2x , dx∫02​2x,dx