Question

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.

Answer 1

Answer:

Volume of smaller canister = 763.02 $cm^3$

Surface area of smaller canister = 466.29 $cm^2$

Volume of larger canister = 6104.16 $cm^3$

Surface area of larger canister = 1865.16 $cm^2$

Volume becomes 8 times by doubling the size and surface area becomes 4 times by doubling the size.

Step-by-step explanation:

Given that :

Diameter of Smaller canister = 9 cm

Height of Smaller canister = 12 cm

Larger canister is double the size of smaller one i.e. height and diameter are doubled.

To find:

Volume and surface area of each canister and their comparison.

Solution:

First of all, let us have a look at the formula of volume and surface area of a cylinder.

Volume, $V=\pi r^2h$

Surface Area, $A=2\pi r^2+ 2\pi rh$

where r and h are the radius and height of the cylinder respectively.

Radius is half of diameter.

Radius of smaller canister is given by:

$r_1 = \dfrac{9}{2} = 4.5\ cm$

Height, $h_1 =12\ cm$

Volume, $V_1=\pi (4.5)^2 \times 12 = 763.02\ cm^3$

Surface Area, $A_1 = 2 \pi \times 4.5 ^2 + 2\pi\times 4.5 \times 12 = 466.29 \ cm^2$

Now, Diameter / Radius and height of larger canister are doubled of smaller one.

Radius of larger canister is given by:

$r_2 = \dfrac{9}{2} \times 2 = 9 cm$

Height, $h_2 =12\times 2 = 24\ cm$

Volume, $V_2=\pi (9)^2 \times 24 = 6104.16\ cm^3$

Surface Area, $A_2 = 2 \pi \times 9 ^2 + 2\pi\times 9\times 24= 1865.16 \ cm^2$

Comparing the results, we can easily see that:

$V_2 = 8 \times V_1\\A_2 = 4 \times A_1$

i.e. Volume becomes 8 times by doubling the size and surface area becomes 4 times by doubling the size.