Coffee is sold in two different sized canisters. The smaller canister has a diameter of 9 cm and a height of 12 cm. The larger canister is double the size of the small canister (i. e., the diameter and height are doubled). Calculate the volume and surface area of each canister and compare the results of doubling the dimensions.

Below

Step-by-step explanation:

The canister has a cylindric form

The volume of a cylinder is given by the following formula :

V= r^2 * Pi *h

H is the heigth and r os the radius(half of the diameter)

Let Pi = 3.14

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V= 3.14*4.5^2 * 12

V= 763.02

V = 763 cm^3(after rounding to the nearest unit)

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The surface area of a cylinder is given by the followong formula:

Sa = 3.14*r^2*2 + Pi*d*h

r is the radius, d the diameter and h the heigth

Let Pi= 3.14

Sa= 3.14*4.5^2*2 + 3.14*9*12

Sa= 466.29 cm^2

Sa= 466 cm^2 ( after rounding to the nearest unit

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The dimensions of the second canister are the double of the first one

V= r^2*Pi*h

V= 9^2 *3.14*24

V= 6104.16 cm^3

V= 6104 cm^3 (after rounding to the neatest unit)

Sa= 2*3.14*r^2+ 3.14*d*h

Sa= 2*3.14*9^2 + 3.14*24*18

Sa= 1865.16 cm^2

Sa= 1865 cm^2 (after roundong to the nearest unit)

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The volume and the surface area of the second canister are bigger than the first one

Divide the second volume by the first one :

V2/V1= 6104/763 = 8

We deduce that the voulme of the second canister is greater 8 times than the first one

Do the same for the surface area

Sa2/Sa1 = 1865/466 = 4.002 = 4 (after rounding to the nearest unit)

The second surface area is greater 4 times than the first one

for ex: the reciprocal of 3/4 is 4/3. it is the opposite.

reciprocal definition:

a mathematical expression or function so related to another that their product is one; the quantity obtained by dividing the number one by a given quantity.

step-by-step explanation: