The ratio of the volumes of two similar circular cylinders is 27:64. What is the ratio of the
diameters of their similar bases?

The ratio of their bases = 3√3 : 8

Step-by-step explanation:

Given,

The ratio of the volume of two cylinders is 27:64.

To find the ratio of the diameters of the cylinders of their base.

Formula

Let, the radius and height of a cylinder is r and h. The volume of the cylinder V = πr²h

Let,

Radius of cylinder 1 is R and the radius of the cylinder 2 is r.

The height of the both cylinder is h.

According to the problem,

πR²h= 27a and πr²h= 64a

So,

πR²h : πr²h = 27a:64a

or, R²:r² = 27:64

or, R:r = 3√3 : 8

Hence,

The ratio of their bases = 3√3 : 8

first, we define the variables:

x: number of years after 1950

f (x): amount of vinyl sold.

then, with the variables defined, we have:

68594 vinyl records were sold in 1958 > f (8) = 68594

91299 vinyl records were sold in 1961 > f (11) = 91299

38720 vinyl records were sold in 1952 > f (2) = 38720

161743 vinyl records were sold in 1967 > f (17) = 161743

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step-by-step explanation:

2. angles qrt and qst both measures 156 degrees.

step-by-step explanation:  

we have been given a diagram of a circle and we are told that measure of arc qvt is 156 degrees.  

we can see from our given diagram that angle qrt and angle qst subtends to arc qvt.

since we know that angles subtended by the same arc at the circumference are always equal.

by angle subtended by same arc theorem, measure of angle qrt and angle qst will be equal to the measure of arc qvt.

therefore, angles qrt and qst both measures 156 degrees and 2nd statement is the correct choice.