Oil is contained in two cylindrical containers. Their heights are 25 cm and 18 cm, and their respective radii are 15 cm and 10 cm. Find the cylindrical vessel's radius, which will only hold the oil from the two specified jars and measure 33 cm in height.

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15 cm

16 cm

17 cm

18 cm

answer is A.

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Detailed Solution

Given that the radii of two vessels are 15 cm and 10 cm, respectively and the heights are, respectively, 25 cm and 18 cm.
We know that the volume of the cylinder is

π r 2 h,

where r is the radius of the cylinder and h is its height.
Therefore the total volume of the two vessels can be calculated as,

V = π 15225 + π 10218 = 5625 π + 1800 π = 7425 π cm 3

Given that, the new vessel has a 33 cm height.
Let’s assume the radius of the new vessel is r cm.
Therefore the radius of new vessel can be calculated as,