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Geometric Area and Volume Flashcards

6 cards from real BMST practice questions. Tap to flip, then mark Knew It or Still Learning — missed cards come back until you master them.

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  1. A hollow cylindrical pipe has an outer radius of 8 cm and an inner radius of 5 cm. If the pipe is 20 cm long, what is the volume of material used to make the pipe?

    Answer: 780π cm³

    The volume of material is the volume of the outer cylinder minus the volume of the inner (hollow) cylinder. Outer volume = π(8²)(20) = 1280π cm³. Inner volume = π(5²)(20) = 500π cm³. Material volume = 1280π − 500π = 780π cm³.

  2. A trapezoid has parallel sides of length 7 m and 13 m, and a height of 6 m. If this trapezoid is the base of a prism that is 10 m tall, what is the volume of the prism?

    Answer: 600 m³

    First find the area of the trapezoid base: A = ½(b₁ + b₂)(h) = ½(7 + 13)(6) = ½(20)(6) = 60 m². Then multiply by the prism height: V = 60 × 10 = 600 m³.

  3. A sector of a circle has a central angle of 135° and a radius of 12 cm. What is the area of the sector? (Use π ≈ 3.14159)

    Answer: 169.6 cm²

    Area of a sector = (θ/360°) × πr². Here θ = 135° and r = 12 cm. Area = (135/360) × π(144) = (3/8) × 144π = 54π ≈ 169.6 cm².

  4. A sphere is inscribed in a cube such that the sphere touches each face of the cube. If the cube has a surface area of 216 cm², what is the volume of the sphere?

    Answer: 113.1 cm³

    The cube's surface area = 6s² = 216 cm², so s² = 36, meaning s = 6 cm. The inscribed sphere's diameter equals the side length, so radius r = 3 cm. Volume of sphere = (4/3)πr³ = (4/3)π(27) = 36π ≈ 113.1 cm³.

  5. Two similar cones have surface areas in the ratio 9:25. If the volume of the smaller cone is 108 cm³, what is the volume of the larger cone?

    Answer: 500 cm³

    For similar solids, the ratio of surface areas equals the square of the scale factor, and the ratio of volumes equals the cube of the scale factor. Surface area ratio = 9:25 = (3:5)², so the linear scale factor is 3:5. Volume ratio = (3:5)³ = 27:125. Setting up the proportion: 108/V = 27/125, so V = 108 × (125/27) = 108 × (125/27) = 500 cm³.

  6. A rectangular swimming pool is 25 m long, 10 m wide, and has a sloped bottom: it is 1 m deep at one end and 3 m deep at the other. What is the volume of water the pool holds when completely full?

    Answer: 500 m³

    The pool's cross-section along its length is a trapezoid with parallel sides of 1 m and 3 m, and length (height of trapezoid) of 25 m. Cross-sectional area = ½(1 + 3)(25) = ½(4)(25) = 50 m². Volume = cross-sectional area × width = 50 × 10 = 500 m³.