A cylinder and a cone have the same radius and height. How many times greater is the volume of the cylinder than the volume of the cone? *

Which expression(s) could be used to correctly calculate the volume of this cone (check all that apply)? *
Radius-10m
height-26m

Which expression would correctly calculate the volume of this cylinder? *
radius-4
height-9

How many cubic feet of water will aquarium B hold? *
It is 10 feet wide

How long is the radius of this cylinder? *
height-11
radius-7

How long is the radius of this cylinder? *
radius-8
height-15

What is the volume of this cone in cubic centimeters? *
radius-15
height-16

What is the volume, rounded to the nearest hundredth, of this ball (use 3.14 for Pi)? *
radius-22

9cm

Step-by-step explanation:

I guessed until I got the right answer

question:

could we have options?

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.