All categories

2 years ago

A cone without a base is made from a half-circle of radius 10 cm. Determine the volume of the cone. Explain your reasoning.

Mathematics

1 answer:

DochEvi [55]2 years ago

5 0

Answer:

125π√3/3 cm³ ≈ 226.72 cm³

Step-by-step explanation:

The length of the circular edge of the half-circle is ...

(1/2)C = (1/2)(2πr) = πr = 10π . . . . cm

This is the circumference of the circular edge of the cone, so the radius of the cone is found from ...

C = 2πr

10π = 2πr . . . . fill in the numbers; next, solve for r

r = 5 . . . . cm

The slant height of the cone is the original radius, 10 cm, so the height of the cone from base to apex is found from the Pythagorean theorem.

(10 cm)² = h² + r²

h = √((10 cm)² -(5 cm)²) = 5√3 cm

And the cone's volume is ...

V = 1/3·πr²h = (1/3)π(5 cm)²(5√3 cm)

V = 125π√3/3 cm³ ≈ 226.72 cm³

You might be interested in

In January of 2003(group 1), 1188 out of 1500 spots were bare ground (no vegetation). Find the sample proportion of bare ground

Nikitich [7]

Answer:

$n= 1500$ represent the random sample selected

$X= 1188$ represent the number of pots that were bare ground (no vegetation

$\hat p=\frac{X}{n}$

And replacing we got:

$\hat p=\frac{1188}{1500}= 0.792$

So then the sample proportion of bare ground spots is 0.792 for this sample

Step-by-step explanation:

We have the following info given from the problem:

$n= 1500$ represent the random sample selected

$X= 1188$ represent the number of pots that were bare ground (no vegetation)

And for this case if we want to find the sample proportion of bare ground spots we can use this formula:

$\hat p=\frac{X}{n}$

And replacing we got:

$\hat p=\frac{1188}{1500}= 0.792$

So then the sample proportion of bare ground spots is 0.792 for this sample

7 0

2 years ago

Alexandra and her children went into a grocery store and she bought $7.65 worth of

zalisa [80]

Answer:

$\large \boxed{\text{3 apples and 6 bananas}}$

Step-by-step explanation:

Let a = the number of apples

And b = the number of bananas. Then,

$\begin{array}{rcll}(1) \, 1.75a + 0.40 b & = & 7.65&\\(2)\, \, \, \, \quad \qquad a + b & = &9&\\(3) \, 0.40a + 0.40b & = &3.60&\text{Multiplied (2) by 0.40}\\1.35a & =&4.05\\(4) \, \, \quad \qquad \qquad a & =& \mathbf{3}&\text{Divided each side by 1.35}\\3 + b & = &9& \text{Substituted(4) into (2)}\\b &=& \mathbf{6}&\text{Subtracted 3 from each side}\\\end{array}\\\text{They bought $\large \boxed{\textbf{3 apples and 6 bananas}}$}$

Check:

$\begin{array}{cccl}3(1.75) + 6(0.40) = 7.65 & \qquad & 3 + 6 = 9\\5.25 + 2.40 = 7.65 & \qquad & 9 = 9\\7.65 = 7.65 & \qquad & \\\end{array}$

OK.

3 0

2 years ago

Mia had $22. Then she started to receive $4 a week as an allowance. She plans to save all of her money for a bicycle and draws a

saw5 [17]

Answer:

first y then x because y represents 22 and x represents 4 a week.

8 0

2 years ago

Stephanie has a $40 balance on her credit card. She makes two additional charges to pay $20 for gas and $25 for parking. Then sh

nikdorinn [45]

Answer:

She should have $25 left

Step-by-step explanation:

It she has a total of $40 and you take away the $20 she spent of gas and the $25 she spent for parking she would have -$5 but since she paid $30 back on the card she has a balance of $25

7 0

2 years ago

Read 2 more answers

3.82e+7 in standard form shown in calculator display

ser-zykov [4K]

E+7 means 10^+7
basically move the decimal place 7 placs to right so it would be aprox
38200000.0

3 0

1 year ago

Read 2 more answers