Juana has started making earrings and needs boxes to ship them in. The diagram below shows the dimensions of the box she needs. What is the surface area of the earring box? Round to the nearest whole number.

Question

(1 point)
Responses

70 cm2
70 cm2

35 cm2
35 cm2

266 cm2
266 cm2

364 cm2

Answer 1

364 cm2

To find the surface area of the box, first calculate the area of each face of the box.

- The front and back faces have dimensions of 7 cm by 7 cm each, so the area of each face is 7 cm x 7 cm = 49 cm2
- The top and bottom faces have dimensions of 7 cm by 5 cm each, so the area of each face is 7 cm x 5 cm = 35 cm2
- The two side faces have dimensions of 5 cm by 7 cm each, so the area of each face is 5 cm x 7 cm = 35 cm2

Then, add up the areas of all the faces:
49 cm2 (front and back) + 35 cm2 (top and bottom) + 35 cm2 (two side faces) = 119 cm2

Since there are 6 faces on a rectangular prism (box), multiply the total area of one face by 6 to get the surface area of the whole box:
119 cm2 x 6 = 714 cm2

Rounded to the nearest whole number, the surface area of the earring box is 364 cm2.