Question

Одна цилиндрическая кружка вдвое выше второй зато вторая в полтора раза шире Найдите отношение обьема второй кружки к обьему первой

Answer 1

V1=s1*h1=pi*r1²*h1
V2=s2*h2=pi*r2²*h2;  h1=2*h2, r2=1,5r1⇒
h2=1/2h1
V2=pi*(1,5r1)²*1/2h1
V2/V1=1,5²*1/2=1,125 - отношение объёмов

Answer 2

Calculating the Volume Ratio of Two Cylindrical Mugs

To find the ratio of the volume of the second mug to the volume of the first mug, we can use the formula for the volume of a cylinder, which is given by the equation:

V = πr^2h

Where: - V is the volume of the cylinder - π is a constant approximately equal to 3.14159 - r is the radius of the base of the cylinder - h is the height of the cylinder

Given Information

We are given that the first cylindrical mug is twice as tall as the second mug, and the second mug is one and a half times wider than the first mug.

Calculating the Volume Ratio

Let's assume the dimensions of the first mug are: - Height: h1 - Radius: r1

And the dimensions of the second mug are: - Height: h2 - Radius: r2

From the given information, we can express the relationship between the dimensions of the two mugs as follows: - h1 = 2h2 (the first mug is twice as tall as the second mug) - r2 = 1.5r1 (the second mug is one and a half times wider than the first mug)

Now, let's calculate the volume ratio of the second mug to the first mug using the given information and the formula for the volume of a cylinder.

The volume of the first mug (V1) is given by: V1 = πr1^2h1

The volume of the second mug (V2) is given by: V2 = πr2^2h2

Substituting the given relationships between the dimensions, we get: V1 = πr1^2(2h2) V2 = π(1.5r1)^2h2

Now, we can calculate the ratio of the volume of the second mug to the volume of the first mug: V2/V1 = (π(1.5r1)^2h2) / (πr1^2(2h2))

Simplifying the expression, we get: V2/V1 = (1.5^2 * r1^2 * h2) / (2 * r1^2 * h2)

Solving further, we find: V2/V1 = (2.25/2) = 1.125

Conclusion

The ratio of the volume of the second cylindrical mug to the volume of the first cylindrical mug is 1.125.