Answer:
V = ∫∫∫rdrdθdz integrating from z = 2 to z = 4, r = 0 to √(16 - z²) and θ = 0 to 2π
Step-by-step explanation:
Since we have the radius of the sphere R = 4, we have R² = r² + z² where r = radius of cylinder in z-plane and z = height² of cylinder.
So, r = √(R² - z²)
r = √(4² - z²)
r = √(16 - z²)
Since the region is above the plane z = 2, we integrate z from z = 2 to z = R = 4
Our volume integral in cylindrical coordinates is thus
V = ∫∫∫rdrdθdz integrating from z = 2 to z = 4, r = 0 to √(16 - z²) and θ = 0 to 2π
Answer:
Step-by-step explanation:
We know a triangle adds up to 180 so:
75+36+ ? = 180
111+ ? =180
? = 69
To find out x, we know that a straight line adds up to 180 so again:
x +69 = 180
x = 111
Answer:
700,000
Step-by-step explanation:
So really, in this question, all you care about is the 10,000ths place
The 10,000ths place in this number is 8. Since 8 is greater that four, round up to 700,000
Answer:
The effect of doubling all the dimensions of a triangular pyramid will have on the volume of the pyramid is to increase it by 8 times.
Step-by-step explanation:
i) volume of triangular pyramid = 
Area height
= (Base of triangle perpendicular height of triangle) height
ii) if we double all the dimensions then the three variables((Base of triangle, perpendicular height of triangle, height of pyramid) will be doubled
and the volume of the new pyramid will be 8 times that of the original one.
