Question 14. A carousel makes one complete revolution every 75 seconds. Levi sits on the carousel 4 feet from its center. If the length of a carousel ride is 5 minutes, how many feet did Levi travel? E. 4 F. 16 G. 8π H. 32π

The correct option is;

H. 32·π

Step-by-step explanation:

The given information are;

The time duration for one complete revolution = 75 seconds

The distance from the center of the carousel where Levi sits = 4 feet

The time length of a carousel ride = 5 minutes

Therefore, the number of complete revolutions, n, in a carousel ride of 5 minutes is given by n = (The time length of a carousel ride)/(The time duration for one complete revolution)

n = (5 minutes)/(75 seconds) = (5×60 seconds/minute)/(75 seconds)

n = (300 s)/(75 s) = 4  

The number of complete revolutions - 4

The distance of 4 complete turns from where Levi seats = 4 ×circumference of circle of Levi's motion

∴ The distance of 4 complete turns from where Levi seats = 4 × 2 × π × 4 = 32·π.

answer: ratio of volume of cone (with 3 times the height and equal diameter) to volume of cylinder is 2 to 1. the value of π is not used.

step-by-step explanation:

radius is diameter/2 = 4.

area of circle is π r^2.

volume of cylinder is height × area of base = hπr^2 = 3(4^2) π = 48π cubic inches.

not knowing the formula for volume of cone, i calculate it using calculus (which is for calculating things).

volume of cone is integral 0 to h area(y) dy. area(y) is π r(y)^2. r(y) runs r to zero as y runs zero to h, r(0) = r, r(h) = 0.

r(y) = r - r/h y

area(y) = π (r - r/h y)^2 = π (r^2 - 2r^2y/h + r^2y^2/h^2) = π r^2(1-2y/h+y^2/h^2)

antiderivative area(y) = π r^2 (y-y^2/h+y^3/(3h^2))

integral 0 to h = π r^2(h-h^2/h+h^3/(3h^2) - (0)) = π r^2(h - h + h/3) = π r^2(h/3) = π/3 r^2 h

volume of this cone is π/3(4^2)18 cubic inches.

= 6 16 π = 96π cubic inches.

cone has twice the volume, 96/48.

cone height is 6 times the cylinder.

ratio of volume formula: π r^2 cancels.

cone over cylinder ratio is 6h/3 to h, 2 to 1.