Question

practice 6 (from unit 5, lesson 6)
a cube has edge length 3 inches.
a. find the surface area and volume of the cube.
type your answers in the boxes.
surface area: square inches
volume: cubic inches
b. the cube is dilated by a scale factor of 0.5. find the surface area and volume of the image.
type your answers in the boxes.
surface area: square inches
volume: cubic inches

Explanation:

Part (a)

Step1: Surface Area of Cube

The formula for the surface area of a cube is \( SA = 6s^2 \), where \( s \) is the edge length. Here, \( s = 3 \) inches.
\( SA = 6\times(3)^2 = 6\times9 = 54 \) square inches.

Step2: Volume of Cube

The formula for the volume of a cube is \( V = s^3 \). For \( s = 3 \) inches,
\( V = (3)^3 = 27 \) cubic inches.

Part (b)

Step1: New Edge Length after Dilation

The scale factor is \( 0.5 \), so the new edge length \( s' = 3\times0.5 = 1.5 \) inches.

Step2: Surface Area of Dilated Cube

Using the surface area formula \( SA' = 6(s')^2 \), with \( s' = 1.5 \):
\( SA' = 6\times(1.5)^2 = 6\times2.25 = 13.5 \) square inches.

Step3: Volume of Dilated Cube

Using the volume formula \( V' = (s')^3 \), with \( s' = 1.5 \):
\( V' = (1.5)^3 = 3.375 \) cubic inches.

Answer:

Part (a)

Surface Area: \( \boldsymbol{54} \) square inches
Volume: \( \boldsymbol{27} \) cubic inches

Part (b)

Surface Area: \( \boldsymbol{13.5} \) square inches
Volume: \( \boldsymbol{3.375} \) cubic inches