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3 years ago

A cone has a radius of 200 m at its base. The cone is 50 m high. How much space is inside the cone?

Mathematics

1 answer:

Sauron [17]3 years ago

7 0

The question "how much space is inside a solid?" is actually asking about the volume of that solid.

The volume of a cone is given by

$V = \dfrac{1}{3}\pi hr^2$

where h is the height of the cone, and r is its radius.

So, you only need to plug in the values:

$V = \dfrac{1}{3}\pi\cdot 50 \cdot 200^2 = \dfrac{2000000\pi}{3}m^3$

You might be interested in

a boy is standing on a pole of height 14.7m throws a stone upwards. it moves in a vertical line slightly away from the pole and

fomenos

Answer:

The time taken for the upward motion is 1 second. The same time is taken for the downward motion

It reaches a maximum height of 4.9 meters.

Step-by-step explanation:

The equation of motion is:

$x(t) = -4.9t^{2} + 9.8t$

Since the term which multiplies t squared is negative, the graph is concave down, that is, x increases until the vertex, where it reaches it's maximum height, then it decreases.

Vertex of a quadratic equation:

Quadratic equation in the format $x(t) = at^{2} + bt + c$

The vertex is the point $(t_{v}, x(t_{v}))$ , in which

$t_{v} = -\frac{b}{2a}$

In this question:

$x(t) = -4.9t^{2} + 9.8t$

So $a = -4.9, b = 9.8$

Vertex:

$t_{v} = -\frac{9.8}{2*(-4.9)} = 1$

The time taken for the upward motion is 1 second.

$x(t_{v}) = x(1) = 9.8*1 - 4.9*(1)^{2} = 4.9$

It reaches a maximum height of 4.9 meters.

Downward motion:

From the vertex to the ground.

The ground is t when x = 0. So

$-4.9t^{2} + 9.8t = 0$

$4.9t^{2} - 9.8t = 0$

$4.9t(t - 2) = 0$

$4.9t = 0$

$t = 0$

$t - 2 = 0$

$t = 2$

It reaches the ground when t = 2 seconds.

The downward motion started at the vertex, when t = 1.

So the duration of the downward motion is 2 - 1 = 1 second.

5 0

2 years ago

Needs answers <br> Will mark brainliest

Elden [556K]

QUESTION 1:

Required angles are: m<2=75°, m<3=75°, m<4= 105°, m<5= 105°, m<6=75°, m<7=75°, m<8=105°

QUESTION 2:

Required angles are: m<1=100° m<2=80°, m<4= 100°, m<5= 100°, m<6=80°, m<7=80°, m<8=100°

Step-by-step explanation:

Question 1:

if m<1 =105°

We need to find the remaining angles.

The corresponding angles of a traversal are same. so the corresponding angle of <1 is angle 5 So, m<5 = 105°

The vertical angles are also equal. so, vertical angle of <1 is <4. So, m<4 = 105°

Vertical angles of m<5 is m<8 so, m<8=105°

m<1 and m<2 are supplementary angles of each other so their sum will be equal to 180°

So, m<1+m<2=180

105+m<2=180

m<2=75°

Same goes for m<3 and m<4 so, m<3 = 75°

m<5 and m<6 so, m<6 = 75°

m<7 and m<8 so, m<7= 75°

So, required angles are: m<2=75°, m<3=75°, m<4= 105°, m<5= 105°, m<6=75°, m<7=75°, m<8=105°

Question No 2

if m<3=80°

We need to find the remaining angles.

The corresponding angles of a traversal are same. so the corresponding angle of <3 is angle 7 So, m<7 = 80°

The vertical angles are also equal. so, vertical angle of <3 is <2. So, m<2 = 80°

The Vertical angle of <7 is <6 so, m<6= 80°.

m<1 and m<2 are supplementary angles of each other so their sum will be equal to 180°

So, m<1+m<2=180

m<1+80=180

m<1=100°

Same goes for m<3 and m<4 so, m<4 = 100°

m<5 and m<6 so, m<5 = 100°

m<7 and m<8 so, m<8= 100°

So, required angles are: m<1=100° m<2=80°, m<4= 100°, m<5= 100°, m<6=80°, m<7=80°, m<8=100°

Keywords: Traversal of parallel lines

Learn more about traversal of parallel lines at:

#learnwithBrainly

3 0

3 years ago

PLS HELP ASAP PLS PLS PLS

Amanda [17]

0=0

Step-by-step explanation:

4(×+3)=4x+12

4x+12=4x+12

Subtract 12 from both sides of the equation

4x+12-12=4x+12-12

simplify

4x=4x

Subtract 4x from both sides of the equation

4x-4x= 4x-4x

Simplify and combine like terms

0=0

8 0

2 years ago

Read 2 more answers

A phone company charges $0.50 per minute and a connection fee of $1. If you were to represent the total cost y of an x minute ca

klasskru [66]

Answer:

Per minute value fee would be the slope of the line.

Step-by-step explanation:

Given:

Per minute charges by the phone company = $ 0.50

Connection fee (fixed) charged by company = $ 1.0

We have to represent the total cost in terms of y and also explain the slope of the line.

According to the question:

Let the number of minutes be "x" .

And the total cost charged be "y" .

So,

The total cost = (No. of minutes)(Per minute charge) + Connection fee

Re-arranging in term of x and y.

⇒ $total\ cost = (no.\ of\ minutes)(per\ minute\ charge) + connection\ fee$

⇒ $y=0.50(x)+1$ ...equation (i)

Slope- intercept form: $y=m(x) +b$ m is the slope and b is the y-is intercept.

⇒ Comparing equation (i) with the slope- intercept form.

⇒ $m=0.50$ and $b=1$

So,

The slope of the line is 0.50 which is also represented by the per minute value of the call.

Per minute value fee would be the slope of the line.

4 0

3 years ago

Help please! I’ll give you brainlist

11111nata11111 [884]

Answer:

1,007 calories in total

Step-by-step explanation:

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3 years ago