Question

Cups A and B are cone shaped and have heights of `24 cm` and `26 cm` and openings with radii of `10 cm` and `7 cm`, respectively. If cup B is full and its contents are poured into cup A, will cup A overflow? If not how high will cup A be filled?

Answer 1

No overflow , h ≈ 12.74cm

Explanation:

Volume of a cone (V) `=1/3pir^2h`
where h represents height and r , the radius.

`V_A = 1/3pixx10^2xx24 ≈ 2513.274 " cubic cm "`

and `V_B = 1/3pixx7^2xx26 ≈ 1334.13 " cubic cm "`

There will be no overflow since `V_B < V_A`

the volume in cup A will therefore be 1334.13 cubic cm

require to find height with this volume in cup A

`rArr V_A = 1/3pixx10^2xxh = 1334.13`

multiply both sides by 3 to eliminate fraction

thus: `pixx10^2h = 3xx1334.13`

divide both sides by`(pixx10^2)`

`rArr (cancel(pixx10^2)h)/(cancel(pixx10^2)) = (3xx1334.13)/(pixx10^2)`

the height of liquid in cup A ≈ 12.74cm