What is the missing length of a rectangular prism where the height and width are both 9 cm in the surface area is 432 cm²
To find the missing length of a rectangular prism, given the height, width, and surface area, we can use the formula for the surface area of a rectangular prism:
Surface Area = 2*(length*width + length*height + width*height)
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*(length*9 + length*9 + 9*9)
Simplifying the equation:
432 = 2*(18*length + 81)
Dividing both sides of the equation by 2:
216 = 18*length + 81
Subtracting 81 from both sides of the equation:
135 = 18*length
Dividing both sides of the equation by 18:
length = 135/18
Simplifying:
length ≈ 7.5 cm
Therefore, the missing length of the rectangular prism is approximately 7.5 cm.
To find the missing length of a rectangular prism, we need to know either the length or the surface area. In this case, we know that the height and width are both 9 cm and the surface area is 432 cm².
The formula for the surface area of a rectangular prism is:
Surface Area = 2(length × width + length × height + width × height)
Given the dimensions of the prism and the surface area, we can plug in the values into the formula and solve for the missing length.
432 cm² = 2(length × 9 + length × 9 + 9 × 9)
Now, let's simplify the equation:
432 cm² = 2(18length + 81)
Divide both sides of the equation by 2:
216 cm² = 18length + 81
Subtract 81 from both sides of the equation:
135 cm² = 18length
Now, divide both sides of the equation by 18:
7.5 cm = length
Therefore, the missing length of the rectangular prism is 7.5 cm.
Well, let's solve this riddle. The surface area of a rectangular prism can be calculated using the formula: SA = 2lw + 2lh + 2wh, where l, w, and h are the length, width, and height, respectively.
In this case, we know that the width and height are both 9 cm, and the surface area is 432 cm². So, let's plug in the given values:
432 = 2l(9) + 2(9)l + 2(9)(9)
Simplifying this equation:
432 = 18l + 18l + 162
432 = 36l + 162
Subtracting 162 from both sides:
270 = 36l
Dividing both sides by 36:
7.5 = l
So, the missing length of the rectangular prism is 7.5 cm. Hope this answer didn't fall flat!
Let the missing length be x cm.
The formula for the surface area of a rectangular prism is:
SA = 2lw + 2lh + 2wh
We are given that the height and width are both 9 cm, so we can substitute those values in and simplify:
432 = 2lx + 2(9)(x) + 2(9)(l)
432 = 2x(l + 9 + 9)
432 = 2x(l + 18)
216 = x(l + 18)
We don't have enough information to solve for both x and l, but we can use some guess and check. We know that the length, l, must be a multiple of 6 (since 216 is divisible by 6), and it must be greater than 9 (since the missing length cannot be shorter than either the height or width). Let's try some values for l:
If l = 12, then x = 12, and the surface area would be:
SA = 2(12)(9) + 2(12)(9) + 2(9)(9)
SA = 432
So, the missing length is 12 cm.