Solved on Jan 22, 2024

Find the surface area of a box with length $l=27$ feet, width $w=7$ feet, and height $h=9$ feet.

STEP 1

Assumptions
1. The box is a rectangular prism.
2. The length ( $l$ ) of the box is 27 feet.
3. The width ( $w$ ) of the box is 7 feet.
4. The height ( $h$ ) of the box is 9 feet.
5. The surface area ( $SA$ ) of a rectangular prism is calculated by the formula: $SA = 2lw + 2lh + 2wh$

STEP 2

First, we need to identify the formula for the surface area of a rectangular prism.
$SA = 2lw + 2lh + 2wh$

STEP 3

Next, we will plug in the given values for the length ( $l$ ), width ( $w$ ), and height ( $h$ ) into the surface area formula.
$SA = 2(27)(7) + 2(27)(9) + 2(7)(9)$

STEP 4

Now, we will calculate the products of each term.
$SA = 2(189) + 2(243) + 2(63)$

STEP 5

Next, we will multiply each term by 2 to find the individual areas.
$SA = 378 + 486 + 126$

STEP 6

Now, we will add these areas together to find the total surface area of the box.
$SA = 378 + 486 + 126$

STEP 7

Finally, we will calculate the sum to determine the surface area.
$SA = 378 + 486 + 126 = 990$
The surface area of the box is 990 square feet.

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Find the surface area of a box with length $l=27$ feet, width $w=7$ feet, and height $h=9$ feet.

STEP 1

Assumptions
1. The box is a rectangular prism.
2. The length ( $l$ ) of the box is 27 feet.
3. The width ( $w$ ) of the box is 7 feet.
4. The height ( $h$ ) of the box is 9 feet.
5. The surface area ( $SA$ ) of a rectangular prism is calculated by the formula: $SA = 2lw + 2lh + 2wh$

STEP 2

First, we need to identify the formula for the surface area of a rectangular prism.
$SA = 2lw + 2lh + 2wh$

STEP 3

Next, we will plug in the given values for the length ( $l$ ), width ( $w$ ), and height ( $h$ ) into the surface area formula.
$SA = 2(27)(7) + 2(27)(9) + 2(7)(9)$

STEP 4

Now, we will calculate the products of each term.
$SA = 2(189) + 2(243) + 2(63)$

STEP 5

Next, we will multiply each term by 2 to find the individual areas.
$SA = 378 + 486 + 126$

STEP 6

Now, we will add these areas together to find the total surface area of the box.
$SA = 378 + 486 + 126$

STEP 7

Finally, we will calculate the sum to determine the surface area.
$SA = 378 + 486 + 126 = 990$
The surface area of the box is 990 square feet.

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Find the surface area of a box with length l=27l=27l=27 feet, width w=7w=7w=7 feet, and height h=9h=9h=9 feet.

STEP 1

Assumptions1. The box is a rectangular prism.2. The length (lll) of the box is 27 feet.3. The width (www) of the box is 7 feet.4. The height (hhh) of the box is 9 feet.5. The surface area (SASASA) of a rectangular prism is calculated by the formula: SA=2lw+2lh+2whSA = 2lw + 2lh + 2whSA=2lw+2lh+2wh

STEP 2

First, we need to identify the formula for the surface area of a rectangular prism.SA=2lw+2lh+2whSA = 2lw + 2lh + 2whSA=2lw+2lh+2wh

STEP 3

Next, we will plug in the given values for the length (lll), width (www), and height (hhh) into the surface area formula.SA=2(27)(7)+2(27)(9)+2(7)(9)SA = 2(27)(7) + 2(27)(9) + 2(7)(9)SA=2(27)(7)+2(27)(9)+2(7)(9)

STEP 4

Now, we will calculate the products of each term.SA=2(189)+2(243)+2(63)SA = 2(189) + 2(243) + 2(63)SA=2(189)+2(243)+2(63)

STEP 5

Next, we will multiply each term by 2 to find the individual areas.SA=378+486+126SA = 378 + 486 + 126SA=378+486+126

STEP 6

Now, we will add these areas together to find the total surface area of the box.SA=378+486+126SA = 378 + 486 + 126SA=378+486+126

STEP 7

Finally, we will calculate the sum to determine the surface area.SA=378+486+126=990SA = 378 + 486 + 126 = 990SA=378+486+126=990The surface area of the box is 990 square feet.

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Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Find the surface area of a box with length $l=27$ feet, width $w=7$ feet, and height $h=9$ feet.

Assumptions
1. The box is a rectangular prism.
2. The length ( $l$ ) of the box is 27 feet.
3. The width ( $w$ ) of the box is 7 feet.
4. The height ( $h$ ) of the box is 9 feet.
5. The surface area ( $SA$ ) of a rectangular prism is calculated by the formula: $SA = 2lw + 2lh + 2wh$

First, we need to identify the formula for the surface area of a rectangular prism.
$SA = 2lw + 2lh + 2wh$

Next, we will plug in the given values for the length ( $l$ ), width ( $w$ ), and height ( $h$ ) into the surface area formula.
$SA = 2(27)(7) + 2(27)(9) + 2(7)(9)$

Now, we will calculate the products of each term.
$SA = 2(189) + 2(243) + 2(63)$

Next, we will multiply each term by 2 to find the individual areas.
$SA = 378 + 486 + 126$

Now, we will add these areas together to find the total surface area of the box.
$SA = 378 + 486 + 126$

Finally, we will calculate the sum to determine the surface area.
$SA = 378 + 486 + 126 = 990$
The surface area of the box is 990 square feet.