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A water tank in the form of an inverted frustum of a right cone has an altitude of 38 ft., and a slant height of 46 ft. The ratio of the upper and lower radii is 5:4. Compute for the measurement of the shorter radius.

Feb 18, 2020

#1
+109740
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Let the radius of the lower  base   =  R

Using the Pythagorean Theorem.....the  length of the radius of the upper base =

R + √ [46^2 - 38^2]  =  R + √672

So

R + √672           5

_______  =     ____            cross-multiply

R                  4

4 [ R + √672 ]   = 5R

4R  + 4√672  = 5R

4√672  =  R

4 (4√42)  = R

16√42  = R  = length of shorter radius (in feet)

Feb 18, 2020
#2
+531
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A water tank in the form of an inverted frustum of a right cone has an altitude of 38 ft., and a slant height of 46 ft. The ratio of the upper and lower radii is 5:4. Compute for the measurement of the shorter radius.

Height =>      h = 38 ft

Slant height => H = 46 ft

Upper radius  R = ?                         R = D * 5

Lower radius   r = ?                          r = D * 4

Ratio    R : r = 5 : 4

Let the defference of R - r be  D

D = sqrt(H2 - h2)  = sqrt (672)

Feb 18, 2020