Kenneth made a scale model of the great bell tower in london in his scale model the height of te tower is 16 inches the actual height of the great bell tower is 320 feet which scale did kenneth use to create the scale model of the great bell tower

1 : 240

Step-by-step explanation:

Given that:

Actual height of the great bell tower = 320 feet

Height of the great bell tower in the scale model = 16 inches

To find:

Scale used by Kenneth to create the scale model?

Solution:

First of all, let us learn about the scale concept.

Scaling is a method to represent the large buildings or monuments on the paper by making a small drawing of the same.

To make small drawings, we decide a scaling factor by which the original monument is drawn smaller.

First of all, let us convert both the quantities given in the same unit.

We know that:

1 ft = 12 inches

320 ft = inches

Scaling factor = Scale model : Actual height

Scaling factor = 16 inches : inches = 1 : 240

Therefore, the scale used for the scale model is 1 : 240.

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.

i’m sorry but i don’t know sorry