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Anna007 [38]
2 years ago
6

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 c

anister is double the size of the small canister. Calculate the volume and surface area of each canister and compare the results of doubling the dimensions.
Mathematics
1 answer:
SVEN [57.7K]2 years ago
7 0

Answer:

Step-by-step explanation:

Smaller Canister:

Height, h = 12cm

Diameter = 9cm

Radius, r = 4.5 cm

Volume  = \pi r^2h\\

           =\pi \times 4.5^2 \times 12\\\\=243 \pi  \ cm^3

Surface \ area = 2 \pi r(r + h)\\

                    =2 \times  \pi \times 4.5 ( 4.5 + 12)\\\\= \pi \times 9(16.5)\\\\=148.5 \ cm^2

Larger Canister:

Measures double the smaller canister, that is

height, H = 24 cm

Diameter = 18cm

Radius, R = 9cm

Volume = \pi R^2 H\\

           = \pi \times 9^2 \times 24\\\\= \pi \times 81 \times 24 \\\\= 1944 \pi

Surface \ area  = 2 \pi R(R+ H)

                    = \pi \times 2 \times 9 ( 9 + 24) \\\\= \pi \times 18(33)\\\\=594 \pi \ cm^2

Comparing results :

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}

Therefore, volume of larger canister is 8 times the volume of smaller canister.

Surface\ area _{larger} = 2 \pi R(R + H) = 2 \pi(2r)((2r+2h))\\\\

                                                   =2 \ pi \times  2r \times 2 (r+ h)\\\\= 4 \times 2\pi r(r+ h) \\\\= 4 \times surface\ area_{smaller}

Therefore, surface area of larger canister is 4 times the surface area of smaller canister.

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