A cube has an edge measuring 4 inches. What is the surface area of the cube, in inches²?
The surface area of a cube can be found by multiplying the area of one face by 6, since a cube has 6 faces of equal area. Since each face is a square, the area of one face is found by squaring the length of the edge.
Given that the edge measures 4 inches, the area of one face is 4^2 = 16 square inches.
Therefore, the surface area of the cube is 16 * 6 = 96 square inches.
Therefore, the surface area of the cube is 96 inches².
(10+13)(2+7y)
What expression is equal to this one
The expression (10+13)(2+7y) can be simplified using the distributive property of multiplication.
First, distribute the terms (10+13) to both terms within the second parentheses (2+7y):
(10+13)(2+7y) = 10(2+7y) + 13(2+7y)
Then, distribute the terms 10 and 13 to the terms within the second parentheses:
= 10(2) + 10(7y) + 13(2) + 13(7y)
Simplifying further:
= 20 + 70y + 26 + 91y
Combine like terms:
= 146 + 161y
Therefore, the expression (10+13)(2+7y) is equal to 146 + 161y.
To find the surface area of a cube, you need to calculate the area of all six faces and then add them together.
1. Calculate the area of one face: The face of a cube is a square, so use the formula for the area of a square, which is side × side. In this case, the side length is 4 inches, so the area of one face is 4 inches × 4 inches = 16 square inches.
2. Since there are six faces in a cube, multiply the area of one face by 6 to get the total surface area. 16 square inches × 6 = 96 square inches.
Therefore, the surface area of the cube is 96 square inches.