Question

Can someone please answer the question on the image provided? Please, and thank you.

Answer 1

50. 8 cm

51. 12π = 37.7 cm³

52. 113 cubic inches.

53. negative

54. non-linear

Explanation:

50. Determine the height of a cylinder given radius = 3 cm and volume = 72 π cm³.

First we need to remember that the formula to calculate the volume of a cylinder is:

V = π * r² * h

Since know everything in this equation (we know V - 72π - and we know r - 3 -, we obviously know π ), we just need to isolate h and input the data we know.

`h = (V)/(\pi * r^(2) ) = (72 \pi)/(\pi * 3^(2) ) = (72)/(9) = 8`

The height is then 8 cm.

51. Determine the volume of a cone, given radius = 2 cm, height = 9 cm.

First we need to remember that the formula to calculate the volume of a cone is:

V = (π * r² * h) / 3

Then we just have to enter our numbers in it and do the math:

`V= (\pi * r^(2) * h)/(3) = (\pi * 2^(2) * 9)/(3) = 12 \pi = 37.7`

The volume of that cone is equivalent to 12 times π or about 37.7 cm³

52. Determine the volume of a grapefruit with a radius of 3 inches, round to the whole number.

A grapefruit is a sphere, we'll assume it's regular. First we need to remember that the formula to calculate the volume of a sphere is:

V = 4(π * r³) / 3

Then we enter our numbers in it:

`V = (4 * \pi * r^(3))/(3) = (4 * \pi * 3^(3))/(3) = 4 * \pi * 9 = 36 * \pi = 113.097`

The volume of that sphere is 113.09, which we round down to the closest whole number: 113 cubic inches.

53. Determine whether there is a positive, negative or no correlation.

By looking at the graphic, you can see a series of dots downwards. If you were to trace a line following those points, a close approximation, you would have a rather straight line going down the Y axis while going further along the X axis.

If you were to calculate the slope of that imaginary line, you'll has a negative value, because the line is going down.

So, there's a negative correlation: the higher the X value, the lower the Y value.

54. Determine whether there is a linear or non-linear correlation.

By looking at the provided graphic, we can see it shows a curve, with a positive correlation, meaning the greater the X value, the greater the Y value.

However, you can see that it's not a straight line as it was in the previous question, it's a curve.

Since it's a curve, it's not a linear correlation.