Scaling in Three Dimensions: Practice Level 2 | Geometry

Level 2 · Intermediate 0 / 12 answered

Question 1 of 12

1

Similar solids have volumes 192 and 648 cubic cm, in original:image order. An original edge is 10 cm long. How long is its image?

Answer choices for question 1 A $22.5\text{ cm}$ B $33.75\text{ cm}$ C $15\text{ cm}$ D $20\text{ cm}$
2

Similar solids have total surface areas 500 and 980 square cm, in original:image order. The original volume is 500 cubic cm. What is the image volume?

Answer choices for question 2 A $1372\text{ cm}^3$ B $980\text{ cm}^3$ C $700\text{ cm}^3$ D $2500\text{ cm}^3$
3

A similar image has $27/64$ of the original volume. Its total surface area is 162 square cm. What is the original total surface area?

Answer choices for question 3 A $216\text{ cm}^2$ B $384\text{ cm}^2$ C $91.125\text{ cm}^2$ D $288\text{ cm}^2$
4

Every length of a solid increases by $20\%$ . What is the percentage increase in its volume?

Answer choices for question 4 A $20\%$ B $72.8\%$ C $44\%$ D $60\%$
5

A similar image has $12.5\%$ of the original volume. What fraction of the original surface area does it have?

Answer choices for question 5 A $1/8$ B $1/2$ C $1/16$ D $1/4$
6

A closed cube has edge 8 cm. What is its surface-area-to-volume ratio?

Answer choices for question 6 A $4/3\text{ cm}^{-1}$ B $6\text{ cm}^{-1}$ C $3/4\text{ cm}^{-1}$ D $3/4\text{ cm}$
7

Solid A and solid B are similar. B has length factor $5/2$ from A. A has surface-area-to-volume ratio $1.5\text{ cm}^{-1}$ . What is B's ratio?

Answer choices for question 7 A $0.6\text{ cm}^{-1}$ B $3.75\text{ cm}^{-1}$ C $0.24\text{ cm}^{-1}$ D $1.5\text{ cm}^{-1}$
8

A closed rectangular box is 2 by 3 by 4 cm. Only the 4 cm height changes to 12 cm. What is the new total surface area?

Answer choices for question 8 A $156\text{ cm}^2$ B $132\text{ cm}^2$ C $468\text{ cm}^2$ D $52\text{ cm}^2$
9

A right cylinder initially has radius 3 cm and height 5 cm. Its radius doubles while height stays fixed. What are the image-to-original volume and total surface-area factors, in that order?

Answer choices for question 9 A $8$ and $4$ B $4$ and $4$ C $4$ and $11/4$ D $2$ and $2$
10

A rectangular prism has dimensions 4 by 7 by 9 cm. A second has dimensions 10 by 17.5 by 22.5 cm, with corresponding dimensions in order. What is the second-to-first volume factor?

Answer choices for question 10 A $25/4$ B $125/8$ C $5/2$ D $8/125$
11

Two similar solids have corresponding lengths 20 mm and 3 cm, in original:image order. What is the image-to-original surface-area factor?

Answer choices for question 11 A $9/400$ B $3/20$ C $27/8$ D $9/4$
12

Similar solids have total surface areas 72 and 200 square cm, in original:image order. What is the image-to-original volume factor?

Answer choices for question 12 A $125/27$ B $25/9$ C $5/3$ D $27/125$