Calculate the surface area of a right rectangular prism. Each edge length is 15 ft

To calculate the surface area of a right rectangular prism, you can use the formula:

\[ \text{Surface Area} = 2(lw + lh + wh) \]

where \( l \) is the length, \( w \) is the width, and \( h \) is the height of the prism.

Given that each edge is 15 ft, we can assume the prism is a cube where \( l = w = h = 15 \) ft.

Now, substituting these values into the formula:

1. Calculate each term:

   • \( lw = 15 \times 15 = 225 \)
   • \( lh = 15 \times 15 = 225 \)
   • \( wh = 15 \times 15 = 225 \)

2. Add these values:

   • \( lw + lh + wh = 225 + 225 + 225 = 675 \)

3. Multiply by 2:

   • \(\text{Surface Area} = 2 \times 675 = 1350\)

Therefore, the surface area of the right rectangular prism is 1350 square feet.

Caroline needs to find the surface area of a cereal box for an art project. The box is a rectangular prism with a length of 8 inches, a height of 12 inches, and a width of 2 inches. What is its surface area?

To calculate the surface area of a rectangular prism (like a cereal box), you can use the formula:

\[ \text{Surface Area} = 2(lw + lh + wh) \]

where:

• \( l \) is the length,
• \( w \) is the width,
• \( h \) is the height.

In this case:

• Length \( l = 8 \) inches,
• Width \( w = 2 \) inches,
• Height \( h = 12 \) inches.

Now, let's substitute these values into the formula:

1. Calculate the products:

   • \( lw = 8 \times 2 = 16 \)
   • \( lh = 8 \times 12 = 96 \)
   • \( wh = 2 \times 12 = 24 \)

2. Add these values together:

   • \( lw + lh + wh = 16 + 96 + 24 = 136 \)

3. Multiply by 2 to get the surface area:

   • \(\text{Surface Area} = 2 \times 136 = 272\)

Therefore, the surface area of the cereal box is 272 square inches.

A roll of wrapping paper measures 25 in.×405 in.
The boxes being wrapped are 16 in.×14 in.×6 in.
How many complete boxes can be wrapped with one roll of wrapping paper

To determine how many complete boxes can be wrapped with one roll of wrapping paper, we first need to calculate the surface area of both the roll of wrapping paper and the boxes.

Step 1: Calculate the surface area of the roll of wrapping paper

The dimensions of the roll are \( 25 \) inches (width) and \( 405 \) inches (length). The surface area is simply the product of these two dimensions:

\[ \text{Surface Area of the roll} = \text{Width} \times \text{Length} = 25 \text{ in} \times 405 \text{ in} = 10125 \text{ square inches} \]

Step 2: Calculate the surface area of one box

The dimensions of the box are \( 16 \) inches (length), \( 14 \) inches (width), and \( 6 \) inches (height). The surface area of a rectangular prism can be calculated using the formula:

\[ \text{Surface Area} = 2(lw + lh + wh) \]

Substituting the dimensions of the box into the formula:

1. Calculate each product:

   • \( lw = 16 \times 14 = 224 \)
   • \( lh = 16 \times 6 = 96 \)
   • \( wh = 14 \times 6 = 84 \)

2. Add these values together:

   • \( lw + lh + wh = 224 + 96 + 84 = 404 \)

3. Multiply by 2 to get the surface area:

   • \(\text{Surface Area of the box} = 2 \times 404 = 808 \text{ square inches}\)

Step 3: Determine how many boxes can be wrapped

Now, we can find out how many complete boxes can be wrapped by dividing the surface area of the roll of wrapping paper by the surface area of one box:

\[ \text{Number of boxes} = \frac{\text{Surface Area of the roll}}{\text{Surface Area of one box}} = \frac{10125}{808} \approx 12.52 \]

Since we can only wrap complete boxes, we take the whole number:

\[ \text{Complete boxes that can be wrapped} = 12 \]

Therefore, with one roll of wrapping paper, 12 complete boxes can be wrapped.