Cups A and B are cone shaped and have heights of $35 c m$ $35 cm$ and $21 c m$ $21 cm$ and openings with radii of $7 c m$ $7 cm$ and $11 c m$ $11 cm$ , 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?

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Answer 1 · 2018-01-12T04:24:21

Cup A will overflow

To find the quantity inside a cup, we need to find the volume.

and Volume of cone = $\frac{1}{3} π r^{2} h$ $1/3pir^2h$

So volume of cup B = $\frac{1}{3} \times \frac{22}{7} \times 11^{2} \times 21$ $1/3 xx22/7xx11^2xx21$ = $2662 c m^{3}$ $2662cm^3$

Now, this $2662 c m^{3}$ $2662cm^3$ is poured into cupA

Now, volume of cup A = $\frac{1}{3} \times \frac{22}{7} \times 7^{2} \times 35$ $1/3 xx22/7xx7^2xx35$ = $1796.6 c m^{3}$ $1796.6 cm^3$

We can observe that volume of cup A is smaller than that of cup B.

So, cup A will overflow when contents of cup B are poured into cup A.

Cups A and B are cone shaped and have heights of 35cm35 cm and 21cm21 cm and openings with radii of 7cm7 cm and 11cm11 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?