Answer:
Volume of smaller canister = 763.02 [tex]cm^3[/tex]
Surface area of smaller canister = 466.29 [tex]cm^2[/tex]
Volume of larger canister = 6104.16 [tex]cm^3[/tex]
Surface area of larger canister = 1865.16 [tex]cm^2[/tex]
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, [tex]V=\pi r^2h[/tex]
Surface Area, [tex]A=2\pi r^2+ 2\pi rh[/tex]
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:
[tex]r_1 = \dfrac{9}{2} = 4.5\ cm[/tex]
Height, [tex]h_1 =12\ cm[/tex]
Volume, [tex]V_1=\pi (4.5)^2 \times 12 = 763.02\ cm^3[/tex]
Surface Area, [tex]A_1 = 2 \pi \times 4.5 ^2 + 2\pi\times 4.5 \times 12 = 466.29 \ cm^2[/tex]
Now, Diameter / Radius and height of larger canister are doubled of smaller one.
Radius of larger canister is given by:
[tex]r_2 = \dfrac{9}{2} \times 2 = 9 cm[/tex]
Height, [tex]h_2 =12\times 2 = 24\ cm[/tex]
Volume, [tex]V_2=\pi (9)^2 \times 24 = 6104.16\ cm^3[/tex]
Surface Area, [tex]A_2 = 2 \pi \times 9 ^2 + 2\pi\times 9\times 24= 1865.16 \ cm^2[/tex]
Comparing the results, we can easily see that:
[tex]V_2 = 8 \times V_1\\A_2 = 4 \times A_1[/tex]
i.e. Volume becomes 8 times by doubling the size and surface area becomes 4 times by doubling the size.
