Question

part b: volume of regular solids

1. a rectangular prism measures 8 cm × 3 cm × 2 cm.

volume = ______ cm³

1. a cube has a side length of 5.5 cm.

volume = ______ cm³

1. a box measures 4 cm × 7 cm × 2.5 cm.

volume = ______ cm³

1. a prism has dimensions 6 cm × 2.5 cm × 3 cm.

volume = ______ cm³

1. a cube has side length 4.2 cm.

volume = ______ cm³
part c: volume of irregular objects

1. a rock is dropped into a graduated cylinder; water before = 15 ml, water after = 28 ml.

volume = ______ ml

1. a small toy is placed in water; water before = 60 ml, water after = 73.5 ml.

volume = ______ ml

1. a marble is submerged in a graduated cylinder; water before = 12 ml, water after = 14.8 ml.

volume = ______ ml

Explanation:

Question 6

Step1: Recall volume formula for rectangular prism

The volume \( V \) of a rectangular prism is given by \( V = l \times w \times h \), where \( l \) is length, \( w \) is width, and \( h \) is height.

Step2: Substitute the values

Here, \( l = 8 \, \text{cm} \), \( w = 3 \, \text{cm} \), \( h = 2 \, \text{cm} \). So \( V = 8 \times 3 \times 2 \).

Step3: Calculate the product

\( 8 \times 3 = 24 \), then \( 24 \times 2 = 48 \).

Step1: Recall volume formula for cube

The volume \( V \) of a cube is given by \( V = s^3 \), where \( s \) is the side length.

Step2: Substitute the value

Here, \( s = 5.5 \, \text{cm} \). So \( V = (5.5)^3 \).

Step3: Calculate the cube

\( 5.5 \times 5.5 = 30.25 \), then \( 30.25 \times 5.5 = 166.375 \).

Step1: Recall volume formula for rectangular prism (box)

The volume \( V \) of a rectangular prism is \( V = l \times w \times h \).

Step2: Substitute the values

Here, \( l = 4 \, \text{cm} \), \( w = 7 \, \text{cm} \), \( h = 2.5 \, \text{cm} \). So \( V = 4 \times 7 \times 2.5 \).

Step3: Calculate the product

\( 4 \times 7 = 28 \), then \( 28 \times 2.5 = 70 \).

Answer:

\( 48 \)

Question 7