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Dima020 [189]
3 years ago
5

The cross-sectional areas of a right triangular prism and a right cylinder are congruent. The right triangular prism has a heigh

t of 6 units, and the right cylinder has a height of 6 units. Which conclusion can be made from the given information? The volume of the triangular prism is half the volume of the cylinder. The volume of the triangular prism is twice the volume of the cylinder. The volume of the triangular prism is equal to the volume of the cylinder. The volume of the triangular prism is not equal to the volume of the cylinder.
Mathematics
1 answer:
expeople1 [14]3 years ago
3 0

Answer:

The correct answer is:

The volume of the triangular prism is equal to the volume of the cylinder

Step-by-step explanation:

Given that there are two figures

1. A right triangular prism and

2. Right cylinder

Area of cross section of prism is equal to Area of cross section of cylinder.

Let this value be <em>A</em>.

Also given that Height of prism = Height of cylinder = <em>6</em>

Volume of a prism is given as:

V_{Prism} = \text{Area of cross section} \times Height

V_{Prism} = A \times 6 ........ (1)

Cross section of cylinder is a circle.

<em>Area of circle</em> is given as: \pi r^{2}

Area of cross section, A = \pi r^{2}

Volume of cylinder is given as:

V_{Cylinder} = \pi r^{2} h\\\Rightarrow V_{Cylinder} = A \times h\\\Rightarrow V_{Cylinder} = A \times 6 ...... (2)

From equations (1) and (2) we can see that

V_{Prism}=V_{Cylinder}

Hence, the correct answer is:

Volume of prism is equal to the volume of cylinder.

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Examples:

       3 x 2  =  6

       7 x 2  =  14

       Both are greater than  2 .


Counter examples:

        1 x 2  =     2

       -6 x 2  =  -12

        Not greater than  2 .    

         
8 0
3 years ago
the perimeter of a rectangle is 56 m. if the width were doubled and the length were increased by 8 m, then the perimeter would b
Natasha2012 [34]
----------------------------------------------------------------
Define x and y:
----------------------------------------------------------------
Let the length be x.
Let the width be y.

----------------------------------------------------------------
Formula:
----------------------------------------------------------------
Perimeter = 2(Length + Width)

----------------------------------------------------------------
Construct equations and solve for x and y:
----------------------------------------------------------------
2x + 2y = 56            ---------------------- (1)
2(x+8) + 4y = 82     -----------------------(2)

----------------------------------------------------------------
From equation 1:
----------------------------------------------------------------
2x + 2y = 56
x + y = 28
x = 28 - y

----------------------------------------------------------------
From equation 2:
----------------------------------------------------------------
2(x+8) + 4y = 82 
2x + 16 + 4y = 82
2x + 4y = 66
x + 2y = 33

----------------------------------------------------------------
Substitute x = 28 - y into equation 2:
----------------------------------------------------------------
x + 2y = 33
(28 - y) + 2y = 33
28 - y + 2y = 33
y = 5

----------------------------------------------------------------
Substitute y = 5 into equation 1:
----------------------------------------------------------------
x = 28 - y 
x = 28 - 5
x = 23

----------------------------------------------------------------
Find Length and Width
----------------------------------------------------------------
Length = x = 23 m
Width = y = 5m

----------------------------------------------------------------
Answer: Length = 23m and Width = 5m
----------------------------------------------------------------
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AleksAgata [21]

Answer:

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Step-by-step explanation:

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I need help..Please make it correct..
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Step-by-step explanation:

3/13, 5/13, 7/13, 9/13, <u>11/13</u>

3/13

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4 0
3 years ago
Factor x^3 -7x^2 -5x+35 by grouping. what is the resulting expression
Anni [7]

Answer:

(x-7) (x^2-5)

Step-by-step explanation:

x^3 -7x^2 -5x+35

Make 2 groups

x^3 -7x^2      -5x+35

Factor x^2 from the first group and -5 from the second group

x^2 (x-7)       -5(x-7)

Now factor (x-7) out

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