Question

a rectangular carton has length 25 cm, width 16 cm, and height 14 cm. find its a) volume and b) surface area.
volume: cm³ surface area: cm²
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question 5 0/1 pt 4 99 details
a box has length 7 feet, width 8 feet, and height 6 inches. find the volume of the box in cubic feet and in cubic inches.
cubic inches
cubic feet
round your answers to the nearest tenth as needed.

Explanation:

Part 1: Rectangular Carton (Volume and Surface Area)

a) Volume of the Rectangular Carton

Step 1: Recall the formula for the volume of a rectangular prism

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

Step 2: Substitute the given values

Given \( l = 25 \, \text{cm} \), \( w = 16 \, \text{cm} \), and \( h = 14 \, \text{cm} \).
\[
V = 25 \times 16 \times 14
\]

Step 3: Calculate the product

First, \( 25 \times 16 = 400 \). Then, \( 400 \times 14 = 5600 \).

Step 1: Recall the formula for the surface area of a rectangular prism

The surface area \( SA \) of a rectangular prism is given by \( SA = 2(lw + lh + wh) \).

Step 2: Substitute the given values

Given \( l = 25 \, \text{cm} \), \( w = 16 \, \text{cm} \), and \( h = 14 \, \text{cm} \).
\[
SA = 2((25 \times 16) + (25 \times 14) + (16 \times 14))
\]

Step 3: Calculate each product inside the parentheses

• \( 25 \times 16 = 400 \)
• \( 25 \times 14 = 350 \)
• \( 16 \times 14 = 224 \)

Step 4: Sum the products

\[
400 + 350 + 224 = 974
\]

Step 5: Multiply by 2

\[
SA = 2 \times 974 = 1948
\]

Step 1: Convert the height to feet

The height is 6 inches. Since 1 foot = 12 inches, \( 6 \, \text{inches} = \frac{6}{12} = 0.5 \, \text{feet} \).

Step 2: Recall the volume formula for a rectangular prism

\( V = l \times w \times h \), where \( l = 7 \, \text{ft} \), \( w = 8 \, \text{ft} \), and \( h = 0.5 \, \text{ft} \).

Step 3: Substitute the values and calculate

\[
V = 7 \times 8 \times 0.5
\]
First, \( 7 \times 8 = 56 \). Then, \( 56 \times 0.5 = 28 \).

Answer:

(Volume): \( 5600 \, \text{cm}^3 \)

b) Surface Area of the Rectangular Carton