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AP Calculus AB Unit 8B: Volumes of Revolution and Cross-Sections — practice questions — page 2

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.

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

Showing questions 31–60 of 66.

The circumference of a circle of radius 7 cm (use π ≈ 22/7):Read the answer and worked solution →The area of a triangle with base b and height h is:Read the answer and worked solution →A square garden of side 20 m is surrounded by a path of uniform width 1 m on the outside. The AREA of the path (only the path, not the garden) is:Read the answer and worked solution →What is the perimeter of an equilateral triangle of side 7 cm?Read the answer and worked solution →The total length around the border of a closed shape is called its:Read the answer and worked solution →The area of a rectangle of length 12 cm and width 5 cm is:Read the answer and worked solution →The Greek letter that represents the ratio of a circle's circumference to its diameter is:Read the answer and worked solution →The perimeter of a rectangle with length a and width b is:Read the answer and worked solution →If $P(A)=0.3$, $P(B)=0.4$ and A, B are mutually exclusive, then $P(A\cup B)$ is:Read the answer and worked solution →The value of $\cos 180^\circ$ is:Read the answer and worked solution →The probability of getting an even number on a single throw of a die is:Read the answer and worked solution →The probability of drawing a king from a standard pack of 52 cards is:Read the answer and worked solution →When two dice are thrown, the probability that the sum of the numbers is 7 is:Read the answer and worked solution →The probability of getting at least one head when a coin is tossed twice is:Read the answer and worked solution →The probability of getting a number greater than 4 on a single throw of a die is:Read the answer and worked solution →The value of $\sin\dfrac{\pi}{6}$ is:Read the answer and worked solution →The expansion of $\sin(A+B)$ is:Read the answer and worked solution →The maximum value of $3\sin\theta$ is:Read the answer and worked solution →Compute 99² (without long multiplication, using (a + b)² or (a − b)²):Read the answer and worked solution →Using the identity (2m, m² − 1, m² + 1) for Pythagorean triplets, the triplet generated by m = 4 is:Read the answer and worked solution →Solve for z: 3(5z − 7) − 2(9z − 11) = 4(8z − 13) − 17Read the answer and worked solution →The square root of 0.81 is:Read the answer and worked solution →Square root of 144 is:Read the answer and worked solution →Which of these cannot possibly be the LAST digit (units digit) of a perfect square?Read the answer and worked solution →How many non-square natural numbers lie between 9² and 10² (exclusive of both)?Read the answer and worked solution →What is 35² without direct multiplication?Read the answer and worked solution →By how much does (n+1)² exceed n²?Read the answer and worked solution →A Pythagorean triplet has one member equal to 12, and the OTHER TWO members differ by 2. The triplet is:Read the answer and worked solution →What is the smallest natural number by which 180 must be MULTIPLIED so that the product becomes a perfect square?Read the answer and worked solution →What is the smallest natural number by which 1620 must be DIVIDED so that the quotient is a perfect square?Read the answer and worked solution →

Worked practice questions

The circumference of a circle of radius 7 cm (use π ≈ 22/7):

  1. 22 cm
  2. 33 cm
  3. 44 cm
  4. 154 cm
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Correct answer: C. 44 cm

Circumference = 2πr = 2 × (22/7) × 7 = 44 cm. (Note: 154 cm² is the AREA of this circle, not perimeter — a classic distractor.)

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The area of a triangle with base b and height h is:

  1. b + h
  2. ½ b h
  3. b h
  4. 2 b h
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Correct answer: B. ½ b h

A triangle is exactly HALF the area of a rectangle (or parallelogram) with the same base and height — you can verify by drawing a diagonal of a rectangle and seeing it splits into two equal triangles. **So Area_triangle = ½ × base × height. Units: square units.**

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A square garden of side 20 m is surrounded by a path of uniform width 1 m on the outside. The AREA of the path (only the path, not the garden) is:

  1. 80 m²
  2. 84 m²
  3. 100 m²
  4. 441 m²
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Correct answer: B. 84 m²

Outer square (garden + path) has side 20 + 1 + 1 = 22 m. Outer area = 22² = 484 m². Inner area (garden alone) = 20² = 400 m². Area of path = outer − inner = 484 − 400 = 84 m². (Trick: thinking 'path is 1m wide × 20m × 4 sides = 80 m²' undercounts because it forgets the four corners of the path — each 1×1 = 1 m² — totalling 4 extra → 80 + 4 = 84 m². ✓)

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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