What is the measure of angle CAE??

The radius of the base of the cylinder is 2x cm and the height of the cylinder is h cm.

valentina_108 [34]

Answer:

h = 9x

Step-by-step explanation:

Given: i. for the cylinder, base radius = 2x cm, height = h cm

ii. for the sphere, radius = 3x cm

iii. volume of the cylinder = volume of the sphere

volume of a cylinder is given as;

volume = $\frac{1}{3}$ $\pi$ $r^{2}$ h

where: r is its base radius and h the height

volume of the given cylinder = $\frac{1}{3}$ $\pi$ x $(2x)^{2}$ x h

= $\frac{1}{3}$ $\pi$ x 4 $x^{2}$ x h

= $\frac{4}{3}$ $\pi$ $x^{2}$ h

volume of a sphere = $\frac{4}{3}$ $\pi$ $r^{3}$

where r is the radius.

volume of the given sphere = $\frac{4}{3}$ $\pi$ x $(3x)^{3}$

= $\frac{4}{3}$ $\pi$ x 9 $x^{3}$

= 12 $\pi$ $x^{3}$

Since,

volume of the cylinder = volume of the sphere

Then we have;

$\frac{4}{3}$ $\pi$ $x^{2}$ h = 12 $\pi$ $x^{3}$

4 $\pi$ $x^{2}$ h = 36 $\pi$ $x^{3}$

subtract $x^{2}$ from both sides

4 $\pi$ h = 36 $\pi$ x

divide both sides by 4 $\pi$

h = $\frac{36\pi x}{4\pi }$

= 9x

h = 9x

5 0

2 years ago

Question 1. Solve using linear combination

Natali5045456 [20]

1) 4d = 24
d = 6
answer d

2) 4d = 12
d = 3
answer c

3) y = 0
ordered pair: (-5 , 0)

Hope this helps!

4 0

3 years ago

Recall that in a 30 – 60 – 90 triangle, if the shortest leg measures x units, then the longer leg measures xStartRoot 3 EndRoot

Brums [2.3K]

The area of the shaded region is $\rm (150\sqrt{3} \ - 75\pi ) \ feet^2$ option first is correct.

It is given that a circle is inscribed in a regular hexagon with sides of 10 feet.

It is required to find the shaded area (missing data is attached shown in the picture).

<h3>What is a circle?</h3>

It is defined as the combination of points that and every point has an equal distance from a fixed point ( called the center of a circle).

We have a hexagon with a side length of 10 feet.

We know the area of the hexagon is given by:

$\rm A = \frac{3\sqrt{3} }{2} a^2$ where a is the side length.

$\rm A = \frac{3\sqrt{3} }{2} 10^2$ ⇒ $150\sqrt{3}$ $\rm feet^2$

We have the shortest length = x feet and from the figure:

2x = 10

x = 5 feet

The radius of the circle r = longer leg

$\rm r = x\sqrt{3} \Rightarrow 5\sqrt{3}$ feet

The area of the circle a = $\pi r^2$ ⇒ $\pi (5\sqrt{3} )^2 \Rightarrow 75\pi \ \rm feet^2$

The area of the shaded region = A - a

$\rm =(150\sqrt{3} \ - 75\pi ) \ feet^2$

Thus, the area of the shaded region is $\rm (150\sqrt{3} \ - 75\pi ) \ feet^2$

Learn more about circle here:

brainly.com/question/11833983

7 0

1 year ago

Help help math math math

Alborosie

Answer:

2/15

Step-by-step explanation:

3 0

2 years ago

Read 2 more answers

I really need help. Someone please help me with this.

9966 [12]

Answer:

angles 1, 3, 6, 8 = 142°

angles 2, 4, 5, 7 = 38°

Step-by-step explanation:

Vertical angles and corresponding angles are congruent, as are alternate interior angles. Hence the angles 1, 3, 6, 8 are all congruent:

∠1 = ∠3 = ∠6 = ∠8 = 142°

Each of the remaining angles forms a linear pair with one or another of those, so is its supplement:

∠2 = ∠4 = ∠5 = ∠7 = 180° -142° = 38°

7 0

2 years ago