Alex built a snowman using three snowballs: one small, one medium, and one large, with diameters in the ratio 2:3:5.
Assuming the snowballs are perfectly spherical and stacked vertically with adjacent snowballs sharing a single point of tangency, if the diameter of the medium snowball is 18 inches, what is the maximum height, in feet, of the snowman Alex built using the three snowballs?
Answer (3)
5 3 = x 18
x = 30 in
and
2 3 = y 18
y = 12 in
M a x im u m h e i g h t = 12 + 18 + 30 = 60 in
them
1 in = 12 1 f t
60 in = 5 f t
∴ M a x im u m h e i g h t = 60 in = 5 f t
r a t i o s n o w ba ll s : 2 : 3 : 5 m e d i u m s n o w ba ll − 18 in x − l a r g e s n o w ba ll 5 3 = x 18 3 x = 90 x = 30 in y − s ma ll s n o w ba ll s 3 2 = 18 y 3 y = 36 y = 12 in 12 + 30 + 18 = 60 in 1 in − 12 1 f t 60 in − z f t z = 12 1 ⋅ 60 = 5 f t A n s w er : M a x im u m h e i g h t i s 5 f t
The maximum height of the snowman built by Alex is 5 feet, calculated by summing the diameters of the three snowballs stacked together. The diameters were based on the given ratio of 2:3:5 with the medium snowball set at 18 inches. Converting the total height into feet, we determined it to be 5 feet.
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