## A cylindrical canister of external diameter 32 cm and with walls 1 cm thick is filled with water to a height of 50 cm in the canister. The w

Question

A cylindrical canister of external diameter 32 cm and with walls 1 cm thick is filled with water to a height of 50 cm in the canister. The water is then poured into a second cylindrical canister with external diameter 52 cm and with walls 1 cm thick. Assuming that the water does not overfill the canister, to what height does the water fill the second canister?

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3 months 2022-02-17T17:01:38+00:00 2 Answers 0 views 0

Yeah, what they said above.

Step-by-step explanation:

$$\frac{1550}{51}$$ cm

Step-by-step explanation:

For the first cylindrical canister:

Let D, R denotes the external diameter and external radius.

Ler r denotes internal radius of the canister.

Let H denotes the height upto which the cylindrical canister contains water.

D = 32 cm

R = D/2 =32/2 = 16 cm

r = R – 1 = 16 – 1 = 15 cm

H = 50 cm

Volume of the first cylindrical canister = $$\pi \left ( R^2-r^2 \right )H=\pi\left ( 16^2-15^2 \right )50=\pi\left ( 256-225 \right )50=1550\pi\,\,cm^3$$

For the second cylinderical canister:

Let D’, R’ denotes the external diameter and external radius.

Ler r’ denotes internal radius of the canister.

Let x denotes the height of the second cylindrical canister.

D’ = 52 cm

R’ = D’/2 = 52/2 = 26 cm

r’ = R’ – 1 = 26 – 1 = 25 cm

Volume of the second cylinderical canister = $$\pi \left ( R’^2-r’^2 \right )H=\pi\left ( 26^2-25^2 \right )x=\pi\left ( 676-625 \right )x=51\pi\,x\,\,cm^3$$

Therefore,

$$x=\frac{1550\pi}{51\pi}=\frac{1550}{51}$$

So,

water fills the second canister to the height of $$\frac{1550}{51}$$ cm.