SOLUTION: A cone is divided into parts A and B. The vertical height of A and B are equal. The volume of cone A is x cm^3. a) express the volume of whole cone in terms of x. b) if the volu

Algebra ->  Volume -> SOLUTION: A cone is divided into parts A and B. The vertical height of A and B are equal. The volume of cone A is x cm^3. a) express the volume of whole cone in terms of x. b) if the volu      Log On


   

Question 1116075: A cone is divided into parts A and B. The vertical height of A and B are equal. The volume of cone A is x cm^3.
a) express the volume of whole cone in terms of x.
b) if the volume of part B is 3500 cm^3. calculate the volume of cone A.
^
/A\
....... here A is a cone (dots indicates circle)
........
/ \
/ B \
.............. here B is frustum ( dots indicates circle)
Answer by greenestamps(13195) About Me  (Show Source):
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The cone A plus the frustum B together form a larger cone with twice the height of cone A.

(a) The cones are similar; since the ratio of the heights of the cones is 2:1, the ratio of the volumes of the cones is 2^3:1^3 or 8:1; so the volume of the whole cone is 8x cm^3.

Answer a): 8x cm^3

(b) Since the volume of the whole cone is 8x and the volume of cone A is x, the volume of frustum B is 7x. If the volume of B is 3500 cm^3, then the volume of cone A is 3500/7 = 500 cm^3.

Answer b): 500 cm^3