Answer:
Step-by-step explanation:
Smaller Canister:
Height, h = 12cm
Diameter = 9cm
Radius, r = 4.5 cm
[tex]Volume = \pi r^2h\\[/tex]
[tex]=\pi \times 4.5^2 \times 12\\\\=243 \pi \ cm^3[/tex]
[tex]Surface \ area = 2 \pi r(r + h)\\[/tex]
[tex]=2 \times \pi \times 4.5 ( 4.5 + 12)\\\\= \pi \times 9(16.5)\\\\=148.5 \ cm^2[/tex]
Larger Canister:
Measures double the smaller canister, that is
height, H = 24 cm
Diameter = 18cm
Radius, R = 9cm
[tex]Volume = \pi R^2 H\\[/tex]
[tex]= \pi \times 9^2 \times 24\\\\= \pi \times 81 \times 24 \\\\= 1944 \pi[/tex]
[tex]Surface \ area = 2 \pi R(R+ H)[/tex]
[tex]= \pi \times 2 \times 9 ( 9 + 24) \\\\= \pi \times 18(33)\\\\=594 \pi \ cm^2[/tex]
Comparing results :
[tex]Volume_{small} = \pi r^2 h\\\\Volume_{large} = \pi R^2 H = \pi(2r)^2(2h) = \pi(4r^2)(2h)= 8 \pi r^2h = 8 \times volume_{small}[/tex]
Therefore, volume of larger canister is 8 times the volume of smaller canister.
[tex]Surface\ area _{larger} = 2 \pi R(R + H) = 2 \pi(2r)((2r+2h))\\\\[/tex]
[tex]=2 \ pi \times 2r \times 2 (r+ h)\\\\= 4 \times 2\pi r(r+ h) \\\\= 4 \times surface\ area_{smaller}[/tex]
Therefore, surface area of larger canister is 4 times the surface area of smaller canister.
