Question

these cubes have sides of 2 cm and 6 cm respectively.

note: picture not drawn to scale

what is the ratio of their volumes?

a. 1 to 9
b. 1 to 3
c. 1 to 27
d. 1 to 4

Explanation:

Calculate the volume of each cube

The volume \(V\) of a cube with side length \(s\) is given by:

$$V = s^3$$

For the smaller cube with side length \(s_1 = 2\text{ cm}\):

$$V_1 = 2^3 = 8\text{ cm}^3$$

For the larger cube with side length \(s_2 = 6\text{ cm}\):

$$V_2 = 6^3 = 216\text{ cm}^3$$

Find the ratio of their volumes

The ratio of the volume of the smaller cube to the larger cube is:

$$\frac{V_1}{V_2} = \frac{8}{216}$$

Simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 8:

$$\frac{8 \div 8}{216 \div 8} = \frac{1}{27}$$

Express the ratio in the required format

The ratio of \(1\) to \(27\) corresponds to option C.

Answer:

• (A) 1 to 9
• (B) 1 to 3
• (C) 1 to 27 (Correct answer)
• (D) 1 to 4