Scaling in Three Dimensions: Practice Level 1 | Geometry

Level 1 · Foundational 0 / 12 answered

Question 1 of 12

1

Similar solids have corresponding lengths 7 cm in the original and 21 cm in the image. What factor takes original lengths to image lengths?

Answer choices for question 1 A $9$ B $3$ C $27$ D $1/3$
2

A solid is resized uniformly by positive length factor 4. What is its surface-area factor?

Answer choices for question 2 A $4$ B $64$ C $8$ D $16$
3

A similar image has length factor $3/2$ . What is its image-to-original volume factor?

Answer choices for question 3 A $27/8$ B $9/4$ C $3/2$ D $8/27$
4

Every length of a solid is multiplied by $1/4$ . What factor multiplies its volume?

Answer choices for question 4 A $1/4$ B $1/16$ C $1/64$ D $1/12$
5

A sphere has radius 4 cm. A similar image has radius 6 cm. What is the surface-area factor?

Answer choices for question 5 A $3/2$ B $9/4$ C $27/8$ D $4/9$
6

Similar solids have corresponding perpendicular heights 6 cm and 9 cm, in original:image order. The original volume is 80 cubic cm. What is the image volume?

Answer choices for question 6 A $270\text{ cm}^3$ B $120\text{ cm}^3$ C $180\text{ cm}^3$ D $640\text{ cm}^3$
7

Surface area is measured in square centimeters and volume in cubic centimeters. What unit does surface area divided by volume have?

Answer choices for question 7 A $\text{cm}$ B $\text{cm}^2$ C No units D $\text{cm}^{-1}$
8

A solid has total surface area 54 square cm and volume 27 cubic cm. What is its surface-area-to-volume ratio?

Answer choices for question 8 A $1/2\text{ cm}^{-1}$ B $2\text{ cm}$ C $2\text{ cm}^{-1}$ D $27\text{ cm}^{-1}$
9

Two similar solids have volume ratio original:image of $1:125$ . What is their corresponding length ratio in the same order?

Answer choices for question 9 A $1:5$ B $1:25$ C $1:125$ D $5:1$
10

Two similar solids have surface-area ratio original:image of $9:16$ . What is their corresponding length ratio in the same order?

Answer choices for question 10 A $9:16$ B $27:64$ C $4:3$ D $3:4$
11

A rectangular box changes from 3 by 4 by 6 cm to 3 by 4 by 12 cm, with the named dimensions corresponding in order. Which description is correct?

Answer choices for question 11 A Uniform enlargement by factor 2. B Uniform enlargement by factor 4. C One-direction stretch; the boxes are not similar. D Congruence with a different orientation.
12

A right cylinder keeps its radius fixed and triples its perpendicular height. What happens to its volume?

Answer choices for question 12 A It increases by factor 9. B It triples. C It increases by factor 27. D It stays the same.