1) The sculptor created a marble basin with an approximate volume of 94,509.6 cubic centimeters - Option D, 2) The approximate area of the heart-shaped cake is 283 square inches - Option B, 3) The length of the wooden frame around the window is 94.3 inches - Option B.

In this question we should make use of geometric formulas for volumes and areas and key information from statement in order to find the right choices.

1) In this case, the volume occupied by the marble water basin ( $V$ ), in cubic centimeters, by subtracting the volume of the hemisphere from the volume of the cylinder:

$V = \pi\cdot R^{2}\cdot h - \frac{2\pi}{3} \cdot r^{3}$ (1)

Where:

$R$ - Radius of the cylinder, in centimeters.
$h$ - Height of the cylinder, in centimeters.
$r$ - Radius of the cylinder, in centimeters.

If we know that $R = 30\,cm$ , $h = 45\,cm$ and $r = 25\,cm$ , then the volume of the marble is:

$V = \pi \cdot (30\,cm)^{2}\cdot (45\,cm) - \frac{2\pi}{3}\cdot (25\,cm)^{3}$

$V \approx 94509.579\,cm^{3}$

The right choice is D.

2) To determine the approximate surface area of the cake covered in red frosting ( $A_{s}$ ), in square inches, we need to find the sum of the surface area of the entire circle and the surface area of the square:

$A_{s} = l^{2} + 2\cdot l\cdot h + \frac{\pi}{4}\cdot D^2 + \pi \cdot D\cdot h$ (2)

Where:

$l$ - Side length of the square, in inches.
$h$ - Height of the cakes, in inches.
$D$ - Diameter of the cakes, in inches.

If we know that $l = 9\,in$ , $h = 3\,in$ and $D = 9\,in$ , then the <em>approximate</em> area covered in red frosting:

$A_{s} = (9\,in)^{2} + 2\cdot (9\,in)\cdot (3\,in) + \frac{\pi}{4}\cdot (9\,in)^{2} + \pi \cdot (9\,in)\cdot (3\,in)$

$A_{s} \approx 283.440\,in^{2}$

The right choice is B.

3) The frame around the window is found by means of the following perimeter formula ( $s$ ), in inches:

$s = \pi\cdot r + 2\cdot h + 2\cdot r$ (3)

Where:

$r$ - Radius, in inches.
$h$ - Height of the rectangle, in inches.

If we know that $r = 9\,in$ and $h = 24\,in$ , then the length of the frame around the window is:

$s = \pi\cdot (9\,in) + 2\cdot (24\,in) + 2\cdot (9\,in)$

$s \approx 94.274\,in$

The right choice is B.

We kindly invite to see question on volumes: brainly.com/question/1578538

7 0

3 years ago

what is a linear function in the form y=mx+b for the line passing through (4.5, -4.25) with y-intercept 2.5?

Murljashka [212]

The M is slope and B is the y-int.
So the B would be +2.5

8 0

4 years ago

Read 2 more answers

Landon has 15 fewer toy cars than his sister. If Landon has 84 toy cars, how many

Naily [24]

Landon's sister has:

<u>99 toy cars</u>

7 0

4 years ago

Read 2 more answers

Suppose a 90% confidence interval for the mean salary of college graduates in a town in Mississippi is given by [$38,737, $50,46

JulsSmile [24]

Answer:

a. The point estimate was of $44,600.

b. The sample size was of 16.

Step-by-step explanation:

Confidence interval concepts:

A confidence interval has two bounds, a lower bound and an upper bound.

A confidence interval is symmetric, which means that the point estimate used is the mid point between these two bounds, that is, the mean of the two bounds.

The margin of error is the difference between the two bounds, divided by 2.

a. What is the point estimate of the mean salary for all college graduates in this town?

Mean of the bounds, so:

(38737+50463)/2 = 44600.

The point estimate was of $44,600.

b. Determine the sample size used for the analysis.

First we need to find the margin of error, so:

$M = \frac{50463-38737}{2} = 5863$