Cups A and B are cone shaped and have heights of $27 c m$ $27 cm$ and $24 c m$ $24 cm$ and openings with radii of $7 c m$ $7 cm$ and $9 c m$ $9 cm$ , 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 · 2018-02-06T21:15:34

See a solution process below:

The formula for the volume of a cone is:

$V = π r^{2} \frac{h}{3}$ $V = pir^2h/3$

The Volume of cup A is:

$V_{a} = π \times {(7 cm)}^{2} \times \frac{27 cm}{3}$ $V_a = pi xx (7"cm")^2 xx (27"cm")/3$

$V_{a} = π \times 49 {cm}^{2} \times 9 cm$ $V_a = pi xx 49"cm"^2 xx 9"cm"$

$V_{a} = π \times 441 {cm}^{3}$ $V_a = pi xx 441"cm"^3$

$V_{a} = 441 {cm}^{3} π$ $V_a = 441"cm"^3pi$

The Volume of cup B is:

$V_{a} = π \times {(9 cm)}^{2} \times \frac{24 cm}{3}$ $V_a = pi xx (9"cm")^2 xx (24"cm")/3$

$V_{a} = π \times 81 {cm}^{2} \times 8 cm$ $V_a = pi xx 81"cm"^2 xx 8"cm"$

$V_{a} = π \times 648 {cm}^{3}$ $V_a = pi xx 648"cm"^3$

$V_{a} = 648 {cm}^{3} π$ $V_a = 648"cm"^3pi$

If a full Cup B is poured into an empty Cup A, then Cup A will overflow

Cups A and B are cone shaped and have heights of 27 cm27cm27 cm and 24 cm24cm24 cm and openings with radii of 7 cm7cm7 cm and 9 cm9cm9 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?