If r= 9 units and x = 4 units, then what is the, №18010394, 25.12.2020 13:51

Mathematics

If r= 9 units and x = 4 units, then what is the volume of the cylinder shown above?

Step-by-step answer

P Answered by Master

Volume of the cylinder is. 1017.36

Step-by-step explanation:

$V=\pi r^2h$ is the area of a cylinder.

Let's plug in our values.

-----

3.14 = pi

9 = radius

x = height

-----

V = (3.14)(9)^2(4)

V = (3.14)(81)(4)

V = (3.14)(324)

V = 1017.36

Mathematics

Look at the cups shown below (images are not drawn to scale): a cone is shown with width 2 inches and height 3 inches, and a cylinder is shown with width 2 inches and height 7 inches. how many more cubic inches of juice will cup b hold than cup a when both are completely full? round your answer to the nearest tenth. 18.8 cubic inches 21.9 cubic inches 25.1 cubic inches 32.6 cubic inches question 9(multiple choice worth 1 points) (03.02 lc) abcd is a rectangle. what is the value of x? rectangle with length 45 feet, width x feet, and diagonal 53

Step-by-step answer

P Answered by PhD

8) 18.8 cubic inches;
9) 28 feet;
10) 1.7 centimeters;
11) 13;
12) 10 centimeters;
13) it is incorrect because the length of the unknown side is the square root of 7,744;
14) square root of 18;
15) 12 miles;
16) 364 centimeters.

Mathematics

So, i have a bunch of math questions and if someone can answer some or all of them that would be great. question 1: a sandwich box is shown with a right triangle side. the right triangle has hypotenuse 12 cm and base 5 cm. what is the approximate minimum height of a shelf in which this box can fit in the position shown in the picture? a) 4.1 centimeters b) 7.0 centimeters c) 8.5 centimeters d) 10.9 centimeters question 2: which of the following shows the length of the third side, in inches, of the triangle? one side of the triangle is labeled as

Step-by-step answer

P Answered by PhD

6

ANSWER TO QUESTION 1.

We use the Pythagoras Theorem to determine the height of the shelf.

Let

be the height of the triangle,

the base and

the hypotenuse.

Then by the Pythagoras Theorem,

h^2+b^2=c^2

We substitute the base, b=5

and the hypotenuse c=12

$h=\sqrt{119}$

h=10.90cm

.

Therefore the approximate minimum height of the shelf should be h=10.90cm

.

the correct answer is A

ANSWER TO QUESTION 2

We apply the Pythagoras Theorem to find the length of the third side.

See diagram

Let the length of the third side be

.

Then

We can now solve for y.

y^2+576=5476

$y=\sqrt{4900}$

y=70

The correct answer is C

ANSWER TO QUESTION 3

We use the Pythagoras Theorem to find the length of PR.

Since PR is the hypotenuse .

|PR|^2=|PQ|^2+|RQ|^2

$|PR|=\sqrt{3600}$

|PR|=60cm

The correct answer is C

See diagram in attachment.

ANSWER TO QUESTION 4

The unknown length is the variable

, which is the hypotenuse of the right angle triangle.

So we use the Pythagoras theorem to find the unknown length.

x^2=24^2+7^2

$\Rightarrow x^2=576+49$

$\Rightarrow x^2=625$

$\Rightarrow x=\sqrt{625}$

$\Rightarrow x=25$

The correct answer is C

ANSWER TO QUESTION 5.

From Pythagoras Theorem, the area of the bigger square is equal to the area of the two smaller squares added together.

See diagram in attachment.

That is x^2=6^2+8^2

.

This implies that,

x^2=36+64

$x=\sqrt{100}$

x=10cm

The correct answer is D

ANSWER TO QUESTION 6

Let

be the length of the unknown leg.

Then from the Pythagoras Theorem,

a^2+144^2=145^2

This implies that;

a^2=145^2-144^2

$a=\sqrt{289}$

a=17 units

The correct answer is option A.

It is incorrect because the length of the unknown side is $\sqrt{289}$ and not 289

.

ANSWER TO QUESTION 7

The diagonal is the hypotenuse of the right angle triangle created by the diagonal, the width and the length of the rectangle.

Since the diagonal is the hypotenuse and the two shorter sides are the width and the length of the rectangle, we can apply the Pythagoras Theorem to find the value of

.

$x=\sqrt{256}$

x=16

The correct answer is B.

ANSWER TO QUESTION 8

Since the width of the cups is 2 inches, it means the radius is half the width.

That is r=1

inch

The volume of a cylinder is given by;

$V=\pi r^2 h$

The cup with the cylindrical shape (B) will hold

$=1^2\times 7 \pi$

$=7 \pi$ cubic inches of juice

The volume of a cone is:

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

The cup with the conical shape cup(A), will hold

$V=\frac{1}{3}\times 1^2 \times 3 \pi$

$V=\pi$ cubic inches of juice

Hence cup B will hold $7\pi -\pi=6\pi=18.8$ cubic inches than cup A.

The correct answer is A
So, i have a bunch of math questions and if someone can answer some or all of them that would be gre

So, i have a bunch of math questions and if someone can answer some or all of them that would be gre

Mathematics

So, i have a bunch of math questions and if someone can answer some or all of them that would be great. question 1: a sandwich box is shown with a right triangle side. the right triangle has hypotenuse 12 cm and base 5 cm. what is the approximate minimum height of a shelf in which this box can fit in the position shown in the picture? a) 4.1 centimeters b) 7.0 centimeters c) 8.5 centimeters d) 10.9 centimeters question 2: which of the following shows the length of the third side, in inches, of the triangle? one side of the triangle is labeled as

Step-by-step answer

P Answered by PhD

6

ANSWER TO QUESTION 1.

We use the Pythagoras Theorem to determine the height of the shelf.

Let

be the height of the triangle,

the base and

the hypotenuse.

Then by the Pythagoras Theorem,

h^2+b^2=c^2

We substitute the base, b=5

and the hypotenuse c=12

$h=\sqrt{119}$

h=10.90cm

.

Therefore the approximate minimum height of the shelf should be h=10.90cm

.

the correct answer is A

ANSWER TO QUESTION 2

We apply the Pythagoras Theorem to find the length of the third side.

See diagram

Let the length of the third side be

.

Then

We can now solve for y.

y^2+576=5476

$y=\sqrt{4900}$

y=70

The correct answer is C

ANSWER TO QUESTION 3

We use the Pythagoras Theorem to find the length of PR.

Since PR is the hypotenuse .

|PR|^2=|PQ|^2+|RQ|^2

$|PR|=\sqrt{3600}$

|PR|=60cm

The correct answer is C

See diagram in attachment.

ANSWER TO QUESTION 4

The unknown length is the variable

, which is the hypotenuse of the right angle triangle.

So we use the Pythagoras theorem to find the unknown length.

x^2=24^2+7^2

$\Rightarrow x^2=576+49$

$\Rightarrow x^2=625$

$\Rightarrow x=\sqrt{625}$

$\Rightarrow x=25$

The correct answer is C

ANSWER TO QUESTION 5.

From Pythagoras Theorem, the area of the bigger square is equal to the area of the two smaller squares added together.

See diagram in attachment.

That is x^2=6^2+8^2

.

This implies that,

x^2=36+64

$x=\sqrt{100}$

x=10cm

The correct answer is D

ANSWER TO QUESTION 6

Let

be the length of the unknown leg.

Then from the Pythagoras Theorem,

a^2+144^2=145^2

This implies that;

a^2=145^2-144^2

$a=\sqrt{289}$

a=17 units

The correct answer is option A.

It is incorrect because the length of the unknown side is $\sqrt{289}$ and not 289

.

ANSWER TO QUESTION 7

The diagonal is the hypotenuse of the right angle triangle created by the diagonal, the width and the length of the rectangle.

Since the diagonal is the hypotenuse and the two shorter sides are the width and the length of the rectangle, we can apply the Pythagoras Theorem to find the value of

.

$x=\sqrt{256}$

x=16

The correct answer is B.

ANSWER TO QUESTION 8

Since the width of the cups is 2 inches, it means the radius is half the width.

That is r=1

inch

The volume of a cylinder is given by;

$V=\pi r^2 h$

The cup with the cylindrical shape (B) will hold

$=1^2\times 7 \pi$

$=7 \pi$ cubic inches of juice

The volume of a cone is:

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

The cup with the conical shape cup(A), will hold

$V=\frac{1}{3}\times 1^2 \times 3 \pi$

$V=\pi$ cubic inches of juice

Hence cup B will hold $7\pi -\pi=6\pi=18.8$ cubic inches than cup A.

The correct answer is A
So, i have a bunch of math questions and if someone can answer some or all of them that would be gre

Mathematics

A cereal company is exploring new cylinder-shaped containers. Two possible containers are shown in the diagram.x is 6 and r=4.5 y is 10.5 and r=3 If both containers have labels covering their lateral surfaces, which container will have less label area and by how much? Container Y by about 42 in.2. Container X by about 28 in.2. Container Y by about 9 in.2. Container X by about 85 in.2.

Step-by-step answer

P Answered by PhD

Container $\rm X$ will have less label area than container $\rm Y$ by about $9\; \rm in$ .

Step-by-step explanation:

A rectangular sheet of paper can be rolled into a cylinder. Conversely, the lateral surface of a cylinder can be unrolled into a rectangle- without changing the area of that surface.

Indeed, the width of that rectangle will be the same as the height of the cylinder. On the other hand, the length of that rectangle should be exactly equal to the circumference of the circles on the top and the bottom of the cylinder. In other words, if a cylinder has a height of and a radius of at the top and the bottom, then its lateral surface can be unrolled into a rectangle of width and length $2\,\pi\, r$ .

Apply this reasoning to both cylinder $\mathrm{X}$ and $\rm Y$ :

For cylinder $\mathrm{X}$ , $h = 6\; \rm in$ while $r = 4.5\; \rm in$ . Therefore, when the lateral side of this cylinder is unrolled:

The width of the rectangle will be $6\; \rm in$ , whileThe length of the rectangle will be $2 \, \pi \times 4.5\; \rm in = 9\, \pi\; \rm in$ .

That corresponds to a lateral surface area of $54\, \pi\; \rm in^2$ .

For cylinder $\rm Y$ , $h = 10.5\; \rm in$ while $r = 3\; \rm in$ . Similarly, when the lateral side of this cylinder is unrolled:

The width of the rectangle will be $10.5\; \rm in$ , whileThe length of the rectangle will be $2\pi\times 3\; \rm in = 6\,\pi \; \rm in$ .

That corresponds to a lateral surface area of $63\,\pi \; \rm in^2$ .

Therefore, the lateral surface area of cylinder $\rm X$ is smaller than that of cylinder $\rm Y$ by $9\,\pi\; \rm in^2$ .