A right pyramid has a height of 3 inches and a square base with side length of 5 inches. What is the volume of the pyramid?
1 answer:
Answer: 25 in³
Step-by-step explanation:
We can calculate the volume of the pyramid by first calculating the volume of a prism with the same dimensions, and then dividing by 3 (all pyramids a volume that's of the volume of a prism with the same dimensions).
The volume of a prism is its base area times its height. The base would be a square, so its area is 5², which is 25. The height is 3 inches, making the prism's volume 75 in³.
The volume of the pyramid would be one-third of this value, which is 75 which is 25 in³.
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<u>Answer-</u> Length of the curve of intersection is 13.5191 sq.units
<u>Solution-</u>
As the equation of the cylinder is in rectangular for, so we have to convert it into parametric form with
x = cos t, y = 2 sin t (∵ 4x² + y² = 4 ⇒ 4cos²t + 4sin²t = 4, then it will satisfy the equation)
Then, substituting these values in the plane equation to get the z parameter,
cos t + 2sin t + z = 2
⇒ z = 2 - cos t - 2sin t
∴
As it is a full revolution around the original cylinder is from 0 to 2π, so we have to integrate from 0 to 2π
∴ Arc length
Now evaluating the integral using calculator,
