Question

wide, and 2 centimeters high. what is the volume of the box?

what is the volume of a rectangular prism with a length of 4 centimeters, a width of 1 centimeter, and a height of 7 centimeter

the base of tim’s closet is a rectangle that is 4 feet long and 2 feet wide. the closet is 7 feet high. what is the volume of tim’s closet?

the base of a rectangular prism is 8 mete long and 5 meters wide. the height of th prism is 3 meters. what is the volume of the prism?

esteban buys cereal in a box that is 10 i high, 7 inches long, and 2 inches wide. is the volume of the cereal box?

what volume formula did you use to

Explanation:

Let's solve each problem one by one using the formula for the volume of a rectangular prism, \( V = l \times w \times h \) (where \( l \) is length, \( w \) is width, and \( h \) is height).

Problem 1 (Box Volume - Partial Text)

Assuming the box has length \( l \), width \( w \), height \( h \) (e.g., if length = 3 cm, width = 3 cm, height = 2 cm as per partial text):

Step1: Identify formula

Volume of rectangular prism: \( V = l \times w \times h \)

Step2: Substitute values (assuming \( l = 3 \), \( w = 3 \), \( h = 2 \))

\( V = 3 \times 3 \times 2 \)
\( V = 18 \) cubic centimeters

Problem 2 (Rectangular Prism: \( l = 4 \) cm, \( w = 1 \) cm, \( h = 7 \) cm)

Step1: Use volume formula

\( V = l \times w \times h \)

Step2: Substitute values

\( V = 4 \times 1 \times 7 \)
\( V = 28 \) cubic centimeters

Problem 3 (Tim’s Closet: \( l = 4 \) ft, \( w = 2 \) ft, \( h = 7 \) ft)

Step1: Apply formula

\( V = l \times w \times h \)

Step2: Calculate

\( V = 4 \times 2 \times 7 \)
\( V = 56 \) cubic feet

Problem 4 (Rectangular Prism: \( l = 8 \) m, \( w = 5 \) m, \( h = 3 \) m)

Step1: Use \( V = l \times w \times h \)

Step2: Compute

\( V = 8 \times 5 \times 3 \)
First, \( 8 \times 5 = 40 \)
Then, \( 40 \times 3 = 120 \)
\( V = 120 \) cubic meters

Problem 5 (Cereal Box: \( l = 7 \) in, \( w = 2 \) in, \( h = 10 \) in)

Step1: Formula \( V = l \times w \times h \)

Step2: Substitute

\( V = 7 \times 2 \times 10 \)
First, \( 7 \times 2 = 14 \)
Then, \( 14 \times 10 = 140 \)
\( V = 140 \) cubic inches

Final Answers (per problem):

1. (Assumed values) \(\boldsymbol{18}\) cubic cm
2. \(\boldsymbol{28}\) cubic cm
3. \(\boldsymbol{56}\) cubic ft
4. \(\boldsymbol{120}\) cubic m
5. \(\boldsymbol{140}\) cubic in

(Note: For the first problem, the exact dimensions were partially visible; the solution above assumes typical values to demonstrate the method. Use the actual given dimensions for precise calculation.)

Answer:

Let's solve each problem one by one using the formula for the volume of a rectangular prism, \( V = l \times w \times h \) (where \( l \) is length, \( w \) is width, and \( h \) is height).

Problem 1 (Box Volume - Partial Text)

Assuming the box has length \( l \), width \( w \), height \( h \) (e.g., if length = 3 cm, width = 3 cm, height = 2 cm as per partial text):

Step1: Identify formula

Volume of rectangular prism: \( V = l \times w \times h \)

Step2: Substitute values (assuming \( l = 3 \), \( w = 3 \), \( h = 2 \))

\( V = 3 \times 3 \times 2 \)
\( V = 18 \) cubic centimeters

Problem 2 (Rectangular Prism: \( l = 4 \) cm, \( w = 1 \) cm, \( h = 7 \) cm)

Step1: Use volume formula

\( V = l \times w \times h \)

Step2: Substitute values

\( V = 4 \times 1 \times 7 \)
\( V = 28 \) cubic centimeters

Problem 3 (Tim’s Closet: \( l = 4 \) ft, \( w = 2 \) ft, \( h = 7 \) ft)

Step1: Apply formula

\( V = l \times w \times h \)

Step2: Calculate

\( V = 4 \times 2 \times 7 \)
\( V = 56 \) cubic feet

Problem 4 (Rectangular Prism: \( l = 8 \) m, \( w = 5 \) m, \( h = 3 \) m)

Step1: Use \( V = l \times w \times h \)

Step2: Compute

\( V = 8 \times 5 \times 3 \)
First, \( 8 \times 5 = 40 \)
Then, \( 40 \times 3 = 120 \)
\( V = 120 \) cubic meters

Problem 5 (Cereal Box: \( l = 7 \) in, \( w = 2 \) in, \( h = 10 \) in)

Step1: Formula \( V = l \times w \times h \)

Step2: Substitute

\( V = 7 \times 2 \times 10 \)
First, \( 7 \times 2 = 14 \)
Then, \( 14 \times 10 = 140 \)
\( V = 140 \) cubic inches

Final Answers (per problem):

1. (Assumed values) \(\boldsymbol{18}\) cubic cm
2. \(\boldsymbol{28}\) cubic cm
3. \(\boldsymbol{56}\) cubic ft
4. \(\boldsymbol{120}\) cubic m
5. \(\boldsymbol{140}\) cubic in

(Note: For the first problem, the exact dimensions were partially visible; the solution above assumes typical values to demonstrate the method. Use the actual given dimensions for precise calculation.)