The inflated

The inflated gymnastic ball should have a diameter of 65 cm. How many times do we have to pump air into a full-blown ball with a bicycle inflator to inflate it if the working volume of the inflator is a cylinder with an inner diameter of 2 cm and a height of 25 cm? (round the result to tens).

Correct answer:

n =  1830

Step-by-step explanation:

$$\begin{gathered} D=65\text{cm} \\ r=D/2=65/2=\frac{65}{2}=32\frac{1}{2}=32.5\text{cm} \\ V=\frac{4}{3}\cdot \pi \cdot r^3=\frac{4}{3}\cdot 3.1416\cdot 32.5^3\doteq 143793.3137{\text{cm}}^3 \\ {D}_2=2\text{cm} \\ h=25\text{cm} \\ {r}_2=D_2/2=2/2=1\text{cm} \\ {V}_2=\pi \cdot r_2^2\cdot h=3.1416\cdot 1^2\cdot 25\doteq 78.5398{\text{cm}}^3 \\ {n}_1=V/V_2=143793.3137/78.5398=\frac{10985}{6}=1830\frac{5}{6}\doteq 1830.8333 \\ n=[n_1/10]\cdot 10=[1830.8333/10]\cdot 10=1830 \end{gathered}$$

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