Melissa has a gerbil that lives in a cage in the shape of a rectangular prism. She wants to put a ramp in the cage to give her gerbil exercise. The cage has a length of 70 cm, a width of 35 cm, and a height of 50 cm. How long does the ramp need to be to fit diagonally in the cage? Round the answer to the nearest tenth. (1 point)
78.6 cm
92.9 cm
60.2 cm
116.3 cm
To find the length of the ramp, we can use the Pythagorean theorem. The length of the ramp is the hypotenuse of a right triangle formed by the length, width, and height of the cage.
The length of the ramp = √(length^2 + width^2 + height^2)
= √(70^2 + 35^2 + 50^2)
= √(4900 + 1225 + 2500)
= √(8625)
≈ 92.9 cm
Therefore, the length of the ramp needs to be approximately 92.9 cm.
To find the length of the ramp needed to fit diagonally in the cage, we need to find the diagonal of the rectangular prism.
The formula to find the diagonal of a rectangular prism is the square root of the sum of the squares of the three dimensions.
Let's apply the formula:
Diagonal = √(length^2 + width^2 + height^2)
= √(70^2 + 35^2 + 50^2)
= √(4900 + 1225 + 2500)
= √(8625)
≈ 92.9 cm
Therefore, the length of the ramp needed to fit diagonally in the cage is approximately 92.9 cm.
So, the correct answer is:
92.9 cm
To find the length of the ramp needed to fit diagonally in the cage, we need to calculate the diagonal of the rectangular prism.
Using the formula for the diagonal of a rectangular prism, which is √(length^2 + width^2 + height^2), we can substitute the given values to find the length of the ramp.
Let's calculate it step by step:
1. Calculate the square of the length: 70 cm * 70 cm = 4900 cm^2
2. Calculate the square of the width: 35 cm * 35 cm = 1225 cm^2
3. Calculate the square of the height: 50 cm * 50 cm = 2500 cm^2
4. Add the three squares together: 4900 cm^2 + 1225 cm^2 + 2500 cm^2 = 8625 cm^2
5. Take the square root of the sum to find the diagonal: √(8625 cm^2) ≈ 92.9 cm
Therefore, the length of the ramp needs to be approximately 92.9 cm.
THIS IS FOR COONEXUS 8TH GRADE!!!!!!!1
1= 15.0 ft
2- 59.5 cm
3- 8.8 cm
4- 9.1 m
5- 9.1 m