Find the arc length of the bolded arc in the picture A) 99.0 ft
C) 756.1 ft
B) 19.6 ft
D) 7.9 ft

  D) 7.9 ft

Step-by-step explanation:

To answer this, you only need to reject the nonsense answers.

The arc length will be more than 5 ft and less than the length of 2 sides of a 5 ft square (10 ft). Only one answer choice falls in that range.

  7.9 ft

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If you like, you can figure 1/4 of the circumference of a circle with radius 5 ft:

  C/4 = (1/4)(2π)(5 ft) = 2.5π ft ≈ 7.854 ft ≈ 7.9 ft

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.