What is the missing length of a rectangular prism where the height and width are both 9 cm and the surface area is 432 cm2?(1 point)
The missing length is 4 cm.
Explanation:
Let the missing length be x.
The surface area of a rectangular prism can be found using the formula:
Surface area = 2lw + 2lh + 2wh
Given:
Height = 9 cm
Width = 9 cm
Surface area = 432 cm2
Substituting these values, we get:
432 = 2x9xw + 2x9xh + 2x9xw
Simplifying, we get:
432 = 36w + 36h
Dividing both sides by 36:
12 = w + h
Substituting the given height and width, we get:
12 = 9 + x
Simplifying, we get:
x = 3
Therefore, the missing length is 4 cm.
To find the missing length of the rectangular prism, we can use the formula for the surface area of a rectangular prism, which is given by:
Surface Area = 2 * (length * height + width * height + length * width)
We are given the height and width to be 9 cm, and the surface area to be 432 cm². Let's substitute these values into the equation and solve for the missing length.
432 = 2 * (length * 9 + 9 * 9 + length * 9)
Simplifying further:
432 = 2 * (9length + 81 + 9length)
432 = 2 * (18length + 81)
Now, distribute the 2 on the right-hand side:
432 = 36length + 162
Move the constant term to the left-hand side:
432 - 162 = 36length
Simplify:
270 = 36length
Finally, divide both sides by 36 to solve for the missing length:
270/36 = length
length ≈ 7.5 cm
Therefore, the missing length of the rectangular prism is approximately 7.5 cm.
To find the missing length of the rectangular prism, we can use the formula for the surface area of a rectangular prism:
Surface Area = 2(height * width + height * length + width * length)
Given that the height and width are both 9 cm, and the surface area is 432 cm², we can substitute these values into the formula:
432 = 2(9 * 9 + 9 * length + 9 * length)
Simplifying:
432 = 2(81 + 18 * length)
Dividing both sides of the equation by 2:
216 = 81 + 18 * length
Subtracting 81 from both sides:
135 = 18 * length
Finally, dividing both sides by 18, we get:
length = 135 / 18
Calculating:
length = 7.5 cm
Therefore, the missing length of the rectangular prism is 7.5 cm.