Find the surface area of a textbook that is 2 in. × 14 in. × 9 in.(1 point)
Responses
344 in.2
344 in. squared
50 in.2
50 in. squared
252 in.2
252 in. squared
172 in.2
172 in. squared
To find the surface area of the textbook, we need to find the area of all six sides and then add them together.
The textbook has six sides: two sides with dimensions 2 in. x 14 in., two sides with dimensions 2 in. x 9 in., and two sides with dimensions 14 in. x 9 in.
The area of the two sides with dimensions 2 in. x 14 in. is 2 in. x 14 in. = 28 in² each.
The area of the two sides with dimensions 2 in. x 9 in. is 2 in. x 9 in. = 18 in² each.
The area of the two sides with dimensions 14 in. x 9 in. is 14 in. x 9 in. = 126 in² each.
Adding up all the areas, we get:
2(28 in²) + 2(18 in²) + 2(126 in²) = 56 in² + 36 in² + 252 in² = 344 in².
Therefore, the surface area of the textbook is 344 in².
Sue is wrapping books to give as gifts. Book A has a length of 6.5 inches, a width of 1 inch, and a height of 8.5 inches. Book B has a length of 5.5 inches, a width of 2 inches, and a height of 8 inches. Based on surface area, which book will require less wrapping paper?(1 point)
Responses
Book A will require less wrapping paper because its surface area is 32.75 in.2
less than the surface area of Book B.
Book A will require less wrapping paper because its surface area is 32.75 in.2
less than the surface area of Book B.
Book B will require less wrapping paper because its surface area is 0.5 in.2
less than the surface area of Book A.
Book B will require less wrapping paper because its surface area is 0.5 in.2
less than the surface area of Book A.
Book B will require less wrapping paper because its surface area is 1.5 in.2
less than the surface area of Book A.
Book B will require less wrapping paper because its surface area is 1.5 in.2
less than the surface area of Book A.
Book A will require less wrapping paper because its surface area is 1.5 in.2
less than the surface area of Book B.
Book A will require less wrapping paper because its surface area is 1.5 in.2
less than the surface area of Book B.
To find the surface area of each book, we need to find the area of all six sides and then add them together.
For Book A:
- The two sides with dimensions 6.5 inches x 1 inch have an area of 6.5 in² each.
- The two sides with dimensions 6.5 inches x 8.5 inches have an area of 55.25 in² each.
- The two sides with dimensions 1 inch x 8.5 inches have an area of 8.5 in² each.
Adding up all the areas, we get:
2(6.5 in²) + 2(55.25 in²) + 2(8.5 in²) = 13 in² + 110.5 in² + 17 in² = 140.5 in².
Therefore, Book A has a surface area of 140.5 in².
For Book B:
- The two sides with dimensions 5.5 inches x 2 inches have an area of 11 in² each.
- The two sides with dimensions 5.5 inches x 8 inches have an area of 44 in² each.
- The two sides with dimensions 2 inches x 8 inches have an area of 16 in² each.
Adding up all the areas, we get:
2(11 in²) + 2(44 in²) + 2(16 in²) = 22 in² + 88 in² + 32 in² = 142 in².
Therefore, Book B has a surface area of 142 in².
Comparing the surface areas, we see that Book A has a surface area of 140.5 in², while Book B has a surface area of 142 in².
Therefore, Book A will require less wrapping paper because its surface area is 1.5 in² less than the surface area of Book B.
Use the image to answer the question.
An illustration shows a 3 D box with length of 27 centimeters labeled as front, a width of 20 centimeters, and height of 20 centimeters.
A box needs to be decorated to use as a prop in a play. The bottom and the back of the box do not need to be decorated. What is the surface area of the box that needs to be decorated?
(1 point)
Responses
1,080 cm
1,080 cm
67 cm2
67 cm squared
1,880 cm2
1,880 cm squared
2,960 cm2
To find the surface area of the box that needs to be decorated, we need to find the area of the front, the top, and the sides of the box.
The front of the box has dimensions of 27 cm (length) x 20 cm (width), so the area of the front is 27 cm x 20 cm = 540 cm².
The top of the box has dimensions of 27 cm (length) x 20 cm (width), so the area of the top is also 27 cm x 20 cm = 540 cm².
The sides of the box have dimensions of 20 cm (width) x 20 cm (height) on both sides, so each side has an area of 20 cm x 20 cm = 400 cm². Since there are two sides, the total area of the sides is 2 x 400 cm² = 800 cm².
Adding up the areas, we get:
540 cm² (front) + 540 cm² (top) + 800 cm² (sides) = 1880 cm².
Therefore, the surface area of the box that needs to be decorated is 1880 cm².