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If you view the chocolates in the box from above, it'll look like as the following figureDeepthi Subbu wrote:3 spherical chocolates are packed in a straight line in a rectangular box that encloses them flush on all sides. If the volume of each of the chocolates is increased by 50% and they are placed in a similar fashion in a new box, what is the ratio of the volume of the new box to that of the original box?
How do you arrive at the height , width and the length of the box to be 2r and 6r?Anurag@Gurome wrote:If you view the chocolates in the box from above, it'll look like as the following figureDeepthi Subbu wrote:3 spherical chocolates are packed in a straight line in a rectangular box that encloses them flush on all sides. If the volume of each of the chocolates is increased by 50% and they are placed in a similar fashion in a new box, what is the ratio of the volume of the new box to that of the original box?
Now, say the radius of each chocolate = r
Hence, height and width of the box = 2r
And, length of the box = 6r
Thus, volume of the box = (r)*(2r)*(6r) = 12r³
Now, volume of each of the chocolates = (4/3)πr³
If volume of each chocolate is increased by 50%, the new volume will be (3/2)*(4/3)πr³ = (4/3)πR³, where R is the new radius of each chocolate. Hence, R³ = (3/2)r³
Ratio of the volume of the new box to that of the original box = (12R³)/(12r³) = R³/r³ = 3/2
Deepthi Subbu wrote:How do you arrive at the height , width and the length of the box to be 2r and 6r?
