What is the area, in square centimeters, of the trapezoid shown below?

8TH GRADE GEOMETRY:100 POINTS+BRAINLIEST: Please answer the question and explain how you did it. Also, please tell me what a "ra

tatyana61 [14]

Answer:

Option B 1 : 3

Step-by-step explanation:

Volume formulas & definitions:

To solve this problem, we must remember the formulas for volume of each shape:

$V_{cylinder}=\pi r^2h\\V_{cone}=\frac{1}{3} \pi r^2 h$ where r represents the radius of the circular part of the shape, and h represents the height of the shape (the plural of height is "heights", and the plural of radius is "radii")

So, when the question states that the shapes "have congruent heights and radii" it means that the height of both objects is the same, and the radius of both objects is the same.

Ratios

To find the ratio of the volume of the cone to the volume of the cylinder, we must setup the ratio. Ratios can be setup as a fraction where the first quantity is the numerator (top of fraction), and the second quantity is the denominator (bottom of the fraction):

$\dfrac{V_{cone}}{V_{cylinder}}=\dfrac{\frac{1}{3} \pi r^2 h} {\pi r^2 h}$

Since the pi, the "r", and the "h" are the same in both the numerator and denominator (and since there is only multiplication & division in the fraction) these common factors can cancel, and reduce the fraction to the following:

$\dfrac{V_{cone}}{V_{cylinder}}=\dfrac{\frac{1}{3}} {1}$

Any number divided by 1 doesn't change, so one-third divided by 1 is still one-third.

$\dfrac{V_{cone}}{V_{cylinder}}=\frac{1}{3}$

Other representations of ratios

Lastly, we must remember that a ratio an also be written with a colon symbol, where the numerator is written first, and the denominator is written second.

So, the ratio of the volume of the cone to the volume of the cylinder is:

1 : 3

7 0

2 years ago

Read 2 more answers

Find the HCF of 96 and 108

White raven [17]

Step-by-step explanation:

it may help you to understand.

5 0

3 years ago

Read 2 more answers

Simplify 16 - 12 ÷ 4 +3 (6-2) show working plz

ira [324]

Answer:

20

Step-by-step explanation:

16-12/4+3(6-2) subtract 6 and 2

16-12/4+3+4 divide 12 and 4

16-3+3+4 subtract 16 and 3

13+3+4 add all 3 numbers

13+7

20

4 0

3 years ago

New York is the 27th largest state in the United States.what percent of the 50 states in the us are larger than New York

Greeley [361]

there are 50 states, NY is the 27th largest so before NY there are other 26 states that are larger than NY.

if we take 50 to be the 100%, what is 26 off of it in percentage?

$\bf \begin{array}{ccll} amount&\%\\ \cline{1-2} 50&100\\ 26&x \end{array}\implies \cfrac{50}{26}=\cfrac{100}{x}\implies \cfrac{25}{13}=\cfrac{100}{x}\implies 25x=1300 \\\\\\ x=\cfrac{1300}{25}\implies x=52$

8 0

4 years ago

What’s the 30th of the linear sequence -5,-2,1,4,7

Vika [28.1K]

The 30th term of the given sequence is 82.

Step-by-step explanation:

The general form of an Arithmetic Progression is a, a + d, a + 2d, a + 3d and so on.
The given linear sequence (-5,-2,1,4,7) is in the form of Arithmetic Progression with a common difference of 3.

-5, -5+3 = -2, -2+3 = 1, 1+3 = 4 and so on.

The nth term is given by the formula nth term = a + (n - 1) d

where

a = first term

d = common difference

To find the 30th term in the given sequence :

The first term, a = -5 and the common difference, d = 3.

30th term = -5 + (30-1) 3

⇒ -5 + (29) 3

⇒ -5 + 87

⇒ 82

Therefore, the 30th term in the given sequence is 82.

7 0

3 years ago