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A conical beaker has a base radius of 8 cm and a height of 15 cm. A conical tank full of acid is a similar shape to the beaker. The beaker can be filled with acid from the tank exactly 1728 times. Work out the base radius and height of the tank

User Dziamid
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1 Answer

5 votes

Explanation:

V = pi×h/3 (R² + Rr + r²) where "V", "h", "R" and "r" are volume, height, larger "rim" radius, and smaller base radius of the conical cylinder (here beaker and tank).

since the beaker and the tank are similar, this means that there is one constant scaling factor for all the corresponding lines between the 2 shapes.

that means that

height of beaker × f = height of tank

has the same "f" as

base radius of beaker × f = base radius of tank.

the same for R ("rim" radius).

and so on.

that means that in the volume formula for the tank the factor "f" is brought in as f³ (product of "f" in "h" and of "f²" in every radius term of the summary terms in the brackets).

so,

Vtank = Vbeaker × f³

therefore,

1728 = f³

f = 12

and the base radius of the tank is

8 × 12 = 96 cm

the height of the tank is

15 × 12 = 180 cm

User DonRumatta
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