What is the missing length of a rectangular prism where the height and width are both 9 cm and the surface area is 432 cm?
Please answer correctly and accurately. I cannot fail this test.
The formula for the surface area of a rectangular prism is SA = 2lw + 2lh + 2wh, where l is the length, w is the width, h is the height, and SA is the surface area.
Substituting the given values, we have:
432 = 2l(9) + 2(9)(9) + 2w(9)
432 = 18l + 162 + 18w
432 - 162 = 18l + 18w
270 = 18(l + w)
15 = l + w
Since the length and width are equal in a rectangular prism, we can substitute l = w and solve for one of them:
15 = 2l
l = 7.5
Therefore, the missing length of the rectangular prism is 7.5 cm.
Well, well, well, looks like we've got a smarty-pants over here! Alright, let's crunch some numbers and solve this puzzle together, shall we?
The surface area of a rectangular prism is given by the formula: SA = 2lw + 2lh + 2wh, where l, w, and h represent the length, width, and height, respectively.
Now let's plug in the given values: SA = 432 cm, w = 9 cm, and h = 9 cm.
Using the formula, we can set up the equation: 432 = 2l(9) + 2(9)(9) + 2(9)l.
Simplifying that equation, we get: 432 = 18l + 162 + 18l.
Combine like terms: 432 = 36l + 162.
Subtract 162 from both sides: 270 = 36l.
Finally, divide both sides by 36: l = 7.5 cm.
Ta-da! The missing length of the rectangular prism is 7.5 cm.
Now that the suspense is over, I hope you aced your test! Good luck, my friend!
To find the missing length of a rectangular prism, we first need to calculate the surface area. The surface area of a rectangular prism is given by the formula:
Surface Area = 2lw + 2lh + 2wh
Given that the height (h) and width (w) are both 9 cm, and the surface area is 432 cm², we can substitute these values into the formula:
432 = 2l(9) + 2(9)(9) + 2(9)l
432 = 18l + 162 + 18l
432 = 36l + 162
Subtracting 162 from both sides:
432 - 162 = 36l
270 = 36l
Next, divide both sides by 36:
270/36 = l
7.5 = l
Therefore, the missing length of the rectangular prism is 7.5 cm.
To find the missing length of a rectangular prism, we first need to calculate the surface area of the prism.
The formula for finding the surface area of a rectangular prism is given by:
Surface Area = 2(length * width + width * height + height * length)
In this case, we are given that the height and width are both 9 cm and the total surface area is 432 cm. Substituting these values into the formula, we have:
432 = 2(length * 9 + 9 * 9 + 9 * length)
Simplifying the equation further, we get:
432 = 2(18length + 81)
Dividing both sides of the equation by 2, we have:
216 = 18length + 81
Subtracting 81 from both sides, we get:
135 = 18length
Finally, dividing both sides by 18, we find:
length = 7.5 cm
Therefore, the missing length of the rectangular prism is 7.5 cm.