Question

★★★ 7. the volume of a shape is the number of cubes it will take, all the same size, to make the figure. each figure is made of stacks of cubes that are 1 centimeter on each side. find the volume of the figures below.

three figures labeled a, b, c, each made of stacked 1-cm cubes

answer: a. ____ cm³ answer: b __ cm³ answer: c ____ cm³

Explanation:

Part a

Step1: Count cubes by layers

Top layer (1st): 1 cube.
Middle layer (2nd): 3 cubes (under the top + adjacent).
Bottom layer (3rd): 6 cubes (base layer).

Step2: Sum the cubes

Total cubes = \( 1 + 3 + 6 = 10 \).

Part b

Step1: Count cubes by layers

Top layer (1st): 1 cube.
Bottom layer (2nd): 7 cubes (base layer + around the top).

Step2: Sum the cubes

Total cubes = \( 1 + 7 = 8 \).

Part c

Step1: Count cubes by layers

Top layer (1st): 1 cube.
Middle layer (2nd): 1 cube (under the top).
Bottom layer (3rd): 5 cubes (base layer).

Step2: Sum the cubes

Total cubes = \( 1 + 1 + 5 = 7 \).

Answer:

s:
a. \( \boldsymbol{10} \) \( \text{cm}^3 \)
b. \( \boldsymbol{8} \) \( \text{cm}^3 \)
c. \( \boldsymbol{7} \) \( \text{cm}^3 \)