If a cone-shaped water cup holds 23 cubic inches and has a radius of 1 inch, what is the height of the cup? use 3.14 to for pi. round your answer to the nearest hundredth. 6.76 inches 18.56 inches 21.97 inches 23.00 inches

  21.97 in

Step-by-step explanation:

Use the formula for the volume of a cone, fill in the given information, and solve for the height.

  V = (1/3)πr²h

  23 in³ = (1/3)(3.14)(1 in)²h . . . . . . . . with given numbers

  3·23 in³/(3.14 in²) = h ≈ 21.97 in . . . . . divide by the coefficient of h

21.97 inches

Step-by-step explanation:

If a cone-shaped water cup holds 23 cubic inches and has a radius of 1 inch, the height of the cup is 21.97 inches.

Round your answer to the nearest hundredth.

1,150 give brainliest

step-by-step explanation

2r= 2300

r =1150

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.