Start learning →

AP Calculus AB Unit 8B: Volumes of Revolution and Cross-Sections — practice questions — page 3

Explore 66 free Unit 8B: Volumes of Revolution and Cross-Sections questions in AP Calculus AB Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

Practise Unit 8B: Volumes of Revolution and Cross-Sections with Quill →

Unit 8B: Volumes of Revolution and Cross-Sections questions and exercises with answers

Showing questions 61–66 of 66.

Compute 105² without direct multiplication:Read the answer and worked solution →Compute the square root of 12.96 (a decimal).Read the answer and worked solution →What is the units digit of (1234)²?Read the answer and worked solution →How many digits will be in the square root of a perfect square with EXACTLY 8 digits?Read the answer and worked solution →Two square fields have areas in the ratio 16 : 9. The ratio of their PERIMETERS is:Read the answer and worked solution →A square garden has area 2025 m². What is its side?Read the answer and worked solution →

Worked practice questions

Compute 105² without direct multiplication:

  1. 10025
  2. 10525
  3. 11025
  4. 11225
Show answer and solution

Correct answer: C. 11025

105² = (100 + 5)² = 100² + 2·100·5 + 5² = 10000 + 1000 + 25 = 11025. Alternatively, using the (a5)² rule: a = 10, a(a+1) = 10·11 = 110 We have so 105² = 11000 + 25. So so 105² = 11025.

Open this question →

Compute the square root of 12.96 (a decimal).

  1. 3.4
  2. 3.5
  3. 3.6
  4. 3.7
Show answer and solution

Correct answer: C. 3.6

12.96 = 1296/100. Now 1296 = 36² (since 36 × 36 = 1296). **So √12.96 = 36/10 = 3.6. Check: 3.6 × 3.6 = 12.96 ✓**

Open this question →

What is the units digit of (1234)²?

  1. 6
  2. 9
  3. 4
  4. 16
Show answer and solution

Correct answer: A. 6

The units digit of n² depends only on the units digit of n. The units digit of 1234 is 4, and 4² = 16, whose units digit is 6. So (1234)² ends in 6. (Option D '16' confuses units digit with the full square of 4 — only the units digit '6' is requested.)

Open this question →

How to practise

  1. Choose a Unit 8B: Volumes of Revolution and Cross-Sections question and try to work out your answer.
  2. Open the question to check the correct answer and read its worked solution.
  3. Continue in the app for bite-sized lessons, explanations and review with Quill. You can start without creating an account.

Put it into practice

Continue with Unit 8B: Volumes of Revolution and Cross-Sections practice for AP Calculus AB. Read explanations as you go. No signup form needed to start.

Practise Unit 8B: Volumes of Revolution and Cross-Sections →

More Mathematics topics

Unit 3B: Implicit Differentiation and Inverse FunctionsUnit 3A: Chain Rule and Composite FunctionsUnit 1A3: Function Composition and InversesUnit 1A1: Relations, Functions and GraphsUnit 1A2: Trigonometric Functions & Inverse TrigUnit 2: Differentiation and Fundamental Derivative RulesUnit 6A: Indefinite Integrals & Fundamental TheoremUnit 1B3: Asymptotic Behavior and Infinite Limits