Back to Exercise: Effects of scaling on area and volume

Effects of Scaling on Area and Volume - Practice Set

Work through each section in order. For multiple-choice problems, select the best answer. Show your work where space is provided.

Grade 10·22 problems·~35 min·Digital SAT Math·topic·sat-geotrig-area-scale

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Recall / Warm-Up

What is the area of a circle with radius 6 cm?

$12\pi$ cm²

$36\pi$ cm²

$6\pi$ cm²

$18\pi$ cm²

What is the volume of a sphere with radius 3 cm? Use $V = \frac{4}{3}\pi r^3$ .

$9\pi$ cm³

$12\pi$ cm³

$36\pi$ cm³

$108\pi$ cm³

Evaluate $k^3$ when $k = 2$ .

Fluency Practice

$Side-by-side rectangles showing a 3×5 original scaled to 6×10, with four small copies fitting inside the large one to illustrate that area scales by k² = 4.$

A rectangle has dimensions 3 cm by 5 cm. Both dimensions are doubled. By what factor does the area increase?

A square has side length 8 m. All dimensions are multiplied by $\frac{1}{2}$ . What is the area of the new square in m²?

$Two spheres with radii 2 cm and 6 cm side by side, showing the k=3 scale factor and illustrating that the large sphere contains 27 times the volume of the small one.$

A sphere has radius 2 cm. A second sphere has radius 6 cm. How many times greater is the volume of the second sphere than the first?

A cylinder has radius 4 cm and height 5 cm. All dimensions are tripled. What is the volume of the new cylinder in cm³? (Use $\pi \approx 3.14$ . Round to the nearest whole number.)

A cylinder has radius $r$ and height $h$ . The radius is doubled, but the height stays the same. By what factor does the volume change?

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