Container NDR

A cone-shaped container with a bottom diameter of 60 cm and a side length of 0.5 m is filled with water. We pour the water into a container with the face of a cylinder with a radius of 3dm and a height of 20cm. Will the cylinder overflow or not be complete? Calculate how much water will overflow or, on the contrary, must be topped up.

Correct answer:

V₁ =  37699.11 cm³
V₂ =  56548.67 cm³
x =  -18849.56 cm³

Step-by-step explanation:

$$\begin{gathered} D=60\text{cm} \\ s=0.50\text{m}\to \text{cm}=0.50\cdot 100\text{cm}=50\text{cm} \\ {r}_1=D/2=60/2=30\text{cm} \\ h=\sqrt{s^2-r_1^2}=\sqrt{50^2-30^2}=40\text{cm} \\ {V}_1=\frac{1}{3}\cdot \pi \cdot r_1^2\cdot h=\frac{1}{3}\cdot 3.1416\cdot 30^2\cdot 40=37699.11{\text{cm}}^3 \end{gathered}$$

$$\begin{gathered} r_2=3\text{dm}\to \text{cm}=3\cdot 10\text{cm}=30\text{cm} \\ {h}_2=20\text{cm} \\ {V}_2=\pi \cdot r_2^2\cdot h_2=3.1416\cdot 30^2\cdot 20=56548.67{\text{cm}}^3 \end{gathered}$$

$x=V_1-V_2=37699.1118-56548.6678=-18849.56{\text{cm}}^3$

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