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

Paul bought a package of 6 spiral notebooks for a total cost of $13.50. which equation represents p, the cost, in dollars, of ea

jek_recluse [69]

6p=13.50

there are 6 notebooks and it costs $13.50 altogether. P represents the cost of one notebook, therefore the equation would be 6p=13.5. It can be rearranged to p=13.5/6

5 0

2 years ago

Ava wants to figure out the average speed she is driving. She starts checking her car’s clock at mile marker 0. It takes her 4 m

VLD [36.1K]

<h2>Answer:</h2>

The average speed of car is:

0.75 miles per minutes.

The equation of line is:

$n=\dfrac{3}{4}t$

<h2>Step-by-step solution:</h2>

The table that describes the time and number of miles marked is given by:

Time Miles

0 0

4 3

8 6

Clearly we could observe that with the increase in time by every 4 minutes the number of mile increases by 3.

i.e. the average speed is calculated as the ratio of change in miles to the change in time.

Hence,

$Average\ Speed=\dfrac{3-0}{4-0}\\\\\\i.e.\\\\\\Average\ Speed=\dfrac{3}{4}=0.75$

Hence, the average speed=0.75 miles per minutes.

Also we will find the equation of the lines that related the miles and time by using the two-point formula.

i.e. any line passing through (a,b) and (c,d) is calculated by using the formula:

$y-b=\dfrac{d-b}{c-a}\times (x-a)$

Here (a,b)=(0,0) and (c,d)=(4,3)

i.e. the equation is given by:

$n-0=\dfrac{3-0}{4-0}\times (t-0)\\\\i.e.\\\\n=\dfrac{3}{4}t$

6 0

2 years ago

Read 2 more answers

In the given the figure above, m∠BAC = 64° and m∠CBA = 56°. Part I: Find the m∠DEC. Part II: Explain the steps you took to arriv

Alex17521 [72]

since the triangles are similar

angle DEC = 60 degrees

3 angles inside a triangle equal 180 degrees

BAC = DCE = 64

CBA = EDC = 56

DEC = 180 -56 -64 = 60 degrees

used angle-angle theorem

6 0

2 years ago

Read 2 more answers

What angle does an arc 6.6cm in length subtends at the centre of a circle of radius 14cm. Use π = 22/7)

aniked [119]

Answer:

STEP 1: Find the circumference:

Circumference = 2πr

Circumference = 2π(14) = 28π cm

............................................................................................

STEP 2: Find the length of the arc:

Length of the arc = 36/360 x 28π

Length of the arc = 8.8 cm

.............................................................................................

Answer: The length of the arc is 8.8 cm

............................................................................................

hope it helpssss

Mark it as brilliant answer plzzz

ФωФ

4 0

2 years ago

Read 2 more answers

Gaia’s gross pay per month is $2,895. Her deductions are listed in the table. Deduction Dollar Amount Federal Income Tax $324 St

bija089 [108]

The correct answer would be $2,310.

5 0

2 years ago

Read 2 more answers