Ask question

Ask question

All categories

3 years ago

7

A hemisphere of radius 7 sits on a horizontal plane. A cylinder stands with its axis vertical, the center of its base at the cen

ter of the sphere, and its top circular rim touching the hemisphere. Find the radius and height of the cylinder of maximum volume.

1 answer:

lozanna [386]3 years ago

5 0

Answer: radius r = 5.72

Height h = 4.04

Step-by-step explanation: Please find the attached file for the solution

You might be interested in

If the average of x, y, and z is 32 and the average of y and z is 27, what is the average of x and 2x?

Orlov [11]

X + y + z = 32 * 3
27 + 27 + x = 96
X = 54
2x = 108
Average of x and 2x = (54+108) / 2 = 164 / 2 = 82
Average of X and 2X = 82

6 0

2 years ago

A sphere is inscribed in a cube with a surface area of 216 square centimeters. What is the volume of the sphere

pentagon [3]

Answer:

$V=298.5cm^3$

Step-by-step explanation:

To find the volume of the sphere we need to know its radius.

And the radius can be found with the information we have about the surface area.

The formula for the surface area is as follows:

$SA=4\pi r^2$

from this formula we clear the radius r:

$r^2=\frac{SA}{4\pi}\\ \\r=\sqrt{\frac{SA}{4\pi} }$

and we substitute the known value of the surface area, and also the value of $\pi$ :

$r=\sqrt{\frac{216cm^2}{4(3.1416)} }\\ \\r=\sqrt{\frac{216cm^2}{12.5664} }\\ \\r=\sqrt{17.1887cm^2}\\ \\r=4.146cm$

and now that we know the radius we find the volume:

$V=\frac{4\pi r^3}{3} \\\\V=\frac{4(3.1416)(4.146cm)^3}{3}\\ \\V=\frac{895.521cm^3}{3}\\ \\V=298.5cm^3$

the volume of the sphere is $298.5cm^3$

7 0

2 years ago

Given the graph of the pre-image and image, identify the correct<br> coordinate transformation.

ziro4ka [17]

The preimage was shifted to the image by a translation 2 units right and 2 units up, so the answer is $(x,y) \longrightarrow (x+2, y+2)$

8 0

1 year ago

Which equation is parallel to the line LaTeX: y=\frac{1}{2}x+3y = 1 2 x + 3and passes through the point (10, -5)?

sukhopar [10]

Answer:

$Equation\ of\ line:\ y=\frac{1}{2}x-10$

Step-by-step explanation:

$Let\ the\ required\ equation\ is\ y=mx+c\\\\where\ m\ is\ the\ slope\ of\ the\ equation\ and\ c\ is\ y-intercept\\\\It\ is\ parallel\ to\ the\ equation\ y=\frac{1}{2}x+3\\\\Hence\ slope\ of\ these\ two\ lines\ will\ be\ same.\\\\Slope\ of\ y=\frac{1}{2}x+3\ is\ \frac{1}{2}\\\\Hence\ slope\ of\ y=mx+c\ is\ \frac{1}{2}\Rightarrow m=\frac{1}{2}\\\\Equation:y=\frac{1}{2}x+c\\\\Line\ passes\ through\ (10,-5).\ Hence\ this\ point\ satisfies\ the\ equation\ of\ line.\\\\-5=\frac{1}{2}\times 10+c$

$-5=-5+c\\\\c=-10$

$Equation\ of\ line:\ y=\frac{1}{2}x-10$

8 0

2 years ago

A sample of 184 light bulbs contained 6 defective bulbs, at this rate ,how many defective bulbs would you expect to find in a sa

givi [52]

184 x 7 = 1288
7 x 6 = 42
so you have 42 <span>defective bulbs</span>

4 0

3 years ago