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mezya [45]
3 years ago
14

A plane, parallel to the base of a cone intersects the cone at the midpoint between points A and B. Determine the area of the cr

oss-section formed by the intersection of the plane and the cone. Leave your answer in terms of pi. 2o height 6 radius
A) 1.5π in2
Eliminate
B) 3π in2
C) 9π in2
D) 36π in2
Mathematics
2 answers:
maksim [4K]3 years ago
8 0

Answer:

Area of cross-section is 9\pi in^{2}

Step-by-step explanation:

Given a cone and a plane parallel to base intersect the cone at the mid point of points between A and B.

We have to find the area of cross-section formed by intersection of the plane and the cone which is a new circle formed.

Given,   height=20 in

             radius=6 in

By mid point theorem i.e the line segment formed by joining the mid points of two side of triangle is parallel to third equal to half of the third side.

therefore new circle formed is of radius 3 in

Hence, area of cross-section formed by intersection of the plane and the cone which is a new circle formed= \pir^{2}

                                                        = 3^{2}\pi

                                                        = 9\piin^{2}


IRINA_888 [86]3 years ago
3 0
Given that point of intersection is at halft ot the heigth, by similarity of triangles, the radius is halft of 6 in, i.e 3 in.

The the area is Pi*r^2 = Pi*(3in)^2 = Pi*9 in^2 = 9Piin^2

This is option C)
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What is the area of a regular octagon with a side length of 6 mm and an apothem length of 7.243 mm? Round your answer to the nea
Harlamova29_29 [7]
OCTA=8, an octagon has 8 sides, thus if one side is 6mm, then all sides, namely the perimeter, is 6+6+6+6+6+6+6+6, or 48.

now, we know what the apothem is.

\bf \textit{area of a regular polygon}\\\\
A=\cfrac{1}{2}ap~~
\begin{cases}
a=apothem\\
p=perimeter\\
-------\\
p=48\\
a=7.243
\end{cases}\implies A=\cfrac{1}{2}(7.243)(48)
5 0
3 years ago
The volume of a prism is 48 cubic centimeters. If the length is 2 centimeters and the width is 4 centimeters. What is the height
Pie

Answer:

6

Step-by-step explanation:

volume is (lwh) since youre trying to find the height just multiply the 2 and 4 together to get 8. Then divide 8 by 48 to get your height.

4 0
3 years ago
What is the intersection when you graph the following equations:
Natasha2012 [34]

Answer:

its -2x

Step-by-step explanation:

7 0
3 years ago
Read 2 more answers
139 students choose to attend one of three after school activities: football, tennis or running.
attashe74 [19]
Answer: 29/139

Explanation:

Total student: 139 (66 boys/73 girls)

Football: 56 student (28 boy/28 girl)

Tennis: 54 student (27 boy/ 27 girl)

Running: 29 student (18 girls/11 boys)

The probability that a student chose running is 29/139

5 0
2 years ago
From a group of 3 men and 4 women, a delegation of 2 is selected. What is the expected number of men in the delegation?
Ostrovityanka [42]

Answer:

The expected number of men in the delegation is 0.86.

Step-by-step explanation:

Number of men = 3

Number of women = 4

A delegation of 2 is selected.

Let X be the number of men selected. So, the possible values of X are 0,1,2.

P(X=0)=\dfrac{^3C_0\times ^4C_2}{^7C_2}=\dfrac{2}{7}

P(X=1)=\dfrac{^3C_1\times ^4C_1}{^7C_2}=\dfrac{4}{7}

P(X=2)=\dfrac{^3C_2\times ^4C_0}{^7C_2}=\dfrac{1}{7}

The expected number of men in the delegation is

E(x)=0\times P(X=0)+1\times P(X=1)+2\times P(X=2)

E(x)=0\times \dfrac{2}{7}+1\times \dfrac{4}{7}+2\times \dfrac{1}{7}

E(x)=\dfrac{6}{7}

E(x)\approx 0.86

Therefore, the expected number of men in the delegation is 0.86.

4 0
3 years ago
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