Question

Две кружки имеют форму цилиндра. Первая кружка в полтора раза выше второй, а вторая втрое шире первой. Во сколько раз объём первой кружки меньше объёма второй?

Answer 1

Высота первой кружки -Н , тогда второй кружки -1,5 Н . Так как вторая кружка в 3 раза шире первой , то её радиус будет равен 3R ( тогда первой - R)     V1=πR²·1.5H        V2=π(3R)²·H
V2\V1=(9πR²H)\(1.5πR²H)=6
В 6 раз объём первой кружки меньше объёма второй кружки

Answer 2

Calculating the Volume Ratio of Two Cylindrical Mugs

To calculate the volume ratio of the first mug to the second mug, we can use the given information about their respective heights and widths.

Given: - The first mug is 1.5 times taller than the second mug. - The second mug is 3 times wider than the first mug.

Calculating the Height and Width Ratios

Let's denote the height of the first mug as h1, the height of the second mug as h2, the width of the first mug as w1, and the width of the second mug as w2.

From the given information, we have: - h1 = 1.5 * h2 - w2 = 3 * w1

Calculating the Volume Ratio

The volume of a cylinder is given by the formula: V = π * r^2 * h, where r is the radius and h is the height.

The volume ratio of the first mug to the second mug can be calculated using the formula: V1 / V2 = (π * r1^2 * h1) / (π * r2^2 * h2)

Since the radius is not given, we can represent the radius of the first mug as r and the radius of the second mug as 3r (assuming the width is directly proportional to the radius).

Simplifying the Volume Ratio

Substituting the given relationships for height and width, we get: V1 / V2 = (π * r^2 * 1.5 * h2) / (π * (3r)^2 * h2)

Simplifying further: V1 / V2 = (1.5 * r^2) / (9 * r^2) V1 / V2 = 1 / 6

Conclusion

The volume of the first mug is 1/6th the volume of the second mug.