Question

A cylindrical jug that carries 5 ℓ of water when it is filled to the brim, has a height of 20 𝑐𝑚. Determine the diameter of the base surface of the jug (in 𝑐𝑚). Round off your answer to the nearest integer.

Answer 1

5L = 5000 cm^3, so since the volume v = πr^2 h, we have

20πr^2 = 5000
r^2 = 250/π
r = √(250/π) = 5√(10/π)
and thus the diameter d = 10√(10/π)

Answer 2

[AI-generated answer — Explain Bot]

To find the diameter of the base surface of the jug, we can use the formula for the volume of a cylinder: V = πr²h, where V is the volume, r is the radius, and h is the height.

In this case, we know the volume V is 5 liters, which can be converted to cubic centimeters since 1 liter is equal to 1000 cubic centimeters. Therefore, we have V = 5000 cm³.

The height of the jug is given as 20 cm, so we have h = 20 cm.

We can rearrange the formula for the volume to solve for the radius:
V = πr²h -> r² = V / (πh) -> r = √(V / πh)

Plugging in the values, we have:
r = √(5000 cm³ / (π * 20 cm))

= √(250 cm² / π)

Calculating further:

r ≈ √79.577 cm²

≈ 8.92 cm

Finally, to find the diameter, we multiply the radius by 2:
d = 2 * 8.92 cm ≈ 17.84 cm

Rounding off to the nearest integer, the diameter of the base surface of the jug is approximately 18 cm.