All categories

3 years ago

The base of a cylinder has an area of 64π in2. If the height of the cylinder is 10 in., what is the total volume?

Mathematics

2 answers:

Stells [14]3 years ago

5 0

Answer:

see explanation

Step-by-step explanation:

The volume (V) of a cylinder is

V = area of base × height

here area of base = 64π and height = 10, hence

V = 64π × 10 = 640π in³ ← exact value

Anastasy [175]3 years ago

3 0

Answer:

V = 3217.0 m3

Step-by-step explanation:

The base area is given and the height is equal to twice the radius.

Use the formula for the area of a circle to solve for the radius of the cylinder.

A=πr2

Substitute 64π for A.

64π=πr2

Divide both sides by π.

64=r2

Take the positive square root of both sides.

8=r

Therefore, the radius is equal to 8 m.

The height is equal to twice the radius.

h=2r

Substitute 8 for r.

h=2⋅8

Simplify.

h=16

Therefore, the height is equal to 16 m.

To find the volume of the cylinder, use the formula for the volume of a cylinder, V=πr2h.

Substitute 8 for r and 16 for h.

V=π⋅82⋅16

Simplify.

V=1024π

Use a calculator to approximate.

V≈3217.0 m3

Therefore, the volume of the cylinder is approximately 3217.0 m3.

You might be interested in

Solve for n. 2n − 35=52n − 35=5

melomori [17]

The answer is n= 35/2

7 0

3 years ago

Read 2 more answers

Suppose you take an SRS of size 1000 of Connecticut students eligible to take the SAT and find that 85% plan to take the SAT dur

nadezda [96]

Answer:

$\mu_{p}=p=0.81$

Step-by-step explanation:

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The population proportion have the following distribution

$p \sim N(p,\sqrt{\frac{p(1-p)}{n}})$

So under the null hypothesis the mean for the population proportion is p

$\mu_{p}=p=0.81$

And the standard deviationis given by:

$\sigma_{p}=\sqrt{\frac{p_0(1-p_o)}{n}}=\sqrt{\frac{0.81(1-0.81)}{1000}}=0.0124$

7 0

3 years ago

The points with coordinates (x, -1), (2,2), and (4,3) lie on the same line. What is the value of x?

borishaifa [10]

Find the slope of the line passing throught the points (2, 2) and (4, 3).

The formula of a slope:

$m=\dfrac{y_2-y_1}{x_2-x_1}$

Substitute:

$m=\dfrac{3-2}{4-2}=\dfrac{1}{2}$

If the point (x, -1) lie on the same line, then the slope of line passing through the points (2, 2) and (x, -1) the same:

Substitute:

$m=\dfrac{-1-2}{x-2}=\dfrac{-3}{x-2}$

We have the equation:

$\dfrac{-3}{x-2}=\dfrac{1}{2}$ <em>cross multiply</em>

$(1)(x-2)=(-3)(2)$

$x-2=-6$ <em>add 2 to both sides</em>

$x=-4$

<h3>Answer: x = -4.</h3>

7 0

3 years ago

In the diagram AB =AD and

Greeley [361]

Answer:

AC ≅ AE

Step-by-step explanation:

According to the SAS Congruence Theorem, for two triangles to be considered equal or congruent, they both must have 2 corresponding sides that are of equal length, and 1 included corresponding angle that is of the same measure in both triangles.

Given that in ∆ABC and ∆ADE, AB ≅ AD, and <BAC ≅ DAE, <em>the additional information we need to prove that ∆ABC ≅ ADE is AC ≅ AE. </em>This will satisfy the SAS Congruence Theorem. As there would be 2 corresponding sides that are congruent, and 1 corresponding angle in both triangles that are congruent to each other.

8 0

3 years ago

A car salesman has 8 used cars for sale. They have a mean price of $4500. What is the total price of all 8 cars?

muminat

Answer:

$36000

Step-by-step explanation:

We have a mean price of $4500 this means that in the 8 cars we have cars with higer and lower prices than $4500 but that if we have to give the same price to 8 cars that would be $4500. Then to know the total price of the all 8 cars we just have to multiply:

$\$4500\cdot 8=$36000$

7 0

3 years ago