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3 years ago

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The volume of a cone is 28.26cm cubed. The radius and height of the cone are equal. What is the radius of the cone? Use 3.14 for

pi

1 answer:

HACTEHA [7]3 years ago

8 0

Answer:

Step-by-step explanation:

Tree

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find the area of the trapezium whose parallel sides are 25 cm and 13 cm The Other sides of a Trapezium are 15 cm and 15 CM

Snezhnost [94]

$\huge\underline{\red{A}\blue{n}\pink{s}\purple{w}\orange{e}\green{r} -}$

Given - <u>A </u><u>trapezium</u><u> </u><u>ABCD </u><u>with </u><u>non </u><u>parallel </u><u>sides </u><u>of </u><u>measure </u><u>1</u><u>5</u><u> </u><u>cm </u><u>each </u><u>!</u><u> </u><u>along </u><u>,</u><u> </u><u>the </u><u>parallel </u><u>sides </u><u>are </u><u>of </u><u>measure </u><u>1</u><u>3</u><u> </u><u>cm </u><u>and </u><u>2</u><u>5</u><u> </u><u>cm</u>

To find - <u>Area </u><u>of </u><u>trapezium</u>

Refer the figure attached ~

In the given figure ,

AB = 25 cm

BC = AD = 15 cm

CD = 13 cm

<u>Construction</u><u> </u><u>-</u>

$draw \: CE \: \parallel \: AD \: \\ and \: CD \: \perp \: AE$

Now , we can clearly see that AECD is a parallelogram !

$\therefore$ AE = CD = 13 cm

Now ,

$AB = AE + BE \\\implies \: BE =AB - AE \\ \implies \: BE = 25 - 13 \\ \implies \: BE = 12 \: cm$

Now , In ∆ BCE ,

$semi \: perimeter \: (s) = \frac{15 + 15 + 12}{2} \\ \\ \implies \: s = \frac{42}{2} = 21 \: cm$

Now , by Heron's formula

$area \: of \: \triangle \: BCE = \sqrt{s(s - a)(s - b)(s - c)} \\ \implies \sqrt{21(21 - 15)(21 - 15)(21 - 12)} \\ \implies \: 21 \times 6 \times 6 \times 9 \\ \implies \: 12 \sqrt{21} \: cm {}^{2}$

Also ,

$area \: of \: \triangle \: = \frac{1}{2} \times base \times height \\ \\\implies 18 \sqrt{21} = \: \frac{1}{\cancel2} \times \cancel12 \times height \\ \\ \implies \: 18 \sqrt{21} = 6 \times height \\ \\ \implies \: height = \frac{\cancel{18} \sqrt{21} }{ \cancel 6} \\ \\ \implies \: height = 3 \sqrt{21} \: cm {}^{2}$

<u>Since </u><u>we've </u><u>obtained </u><u>the </u><u>height </u><u>now </u><u>,</u><u> </u><u>we </u><u>can </u><u>easily </u><u>find </u><u>out </u><u>the </u><u>area </u><u>of </u><u>trapezium </u><u>!</u>

$Area \: of \: trapezium = \frac{1}{2} \times(sum \: of \:parallel \: sides) \times height \\ \\ \implies \: \frac{1}{2} \times (25 + 13) \times 3 \sqrt{21} \\ \\ \implies \: \frac{1}{\cancel2} \times \cancel{38 }\times 3 \sqrt{21} \\ \\ \implies \: 19 \times 3 \sqrt{21} \: cm {}^{2} \\ \\ \implies \: 57 \sqrt{21} \: cm {}^{2}$

hope helpful :D

6 0

2 years ago

Gloria is an artist. She sets a goal to paint 2 paintings every month. The number of paintings Gloria creates depends on the num

BartSMP [9]

Answer:

we get the all equation of given condition $M = 2P+1$ & $P=2M+1$ Step-by-step explanation:

Given that,

Number of painting made by Gloria every month is 2.

Gloria creates depends on the number of paintings p, Gloria paints over m months if she meet her goal.

we have to check all the apply.

According to question,

M is the independent variable and P is dependent variable.

So, Relation formed by given statement is $M =2P$

Case(1): P is increased by 2 as M is increased by 1.

Then, $M+1= 2\times (P+2)$

$M+1= 2P+2$

$M = 2P+1$

This is Equation of the given case(1).

Again, P is the independent variable and M is dependent variable.

∴ $P=2M$

Case (2) M is increased by 2 as P increased by 1.

Then, $P+1=2\times(M+2)$

$P+1=2M+2$

$P=2M+1$

Hence,

we get the all equation of given condition $M = 2P+1$ & $P=2M+1$

4 0

3 years ago

A shopper paid $2.52 for 4.5 pounds of potatoes and $7.75 for 2.5 pounds of broccoli. What is the unit price of each item she bo

Maurinko [17]

<h3>Unit price is $ 0.56 per pound of potatoes</h3><h3>Unit price is $ 3.1 per pound of broccoli</h3>

<em><u>Solution:</u></em>

Given that,

Unit price is the price of 1 unit

$\textrm{Unit Price} = \frac{\textrm{Total cost on n products}}{\textrm{n}}$

<h3><u>Find unit price of potatoes</u></h3>

A shopper paid $2.52 for 4.5 pounds of potatoes

$Unit\ Price = \frac{2.52}{4.5}\\\\Unit\ Price = 0.56$

Thus unit price is $ 0.56 per pound of potatoes

<h3><u>Find unit price of broccoli</u></h3>

$7.75 for 2.5 pounds of broccoli

$Unit\ Price = \frac{7.75}{2.5}\\\\Unit\ Price = 3.1$

Thus unit price is $ 3.1 per pound of broccoli

5 0

4 years ago

Is the binomial a factor of the polynomial nominal function?

Sedbober [7]

The factors for given equation f(x)= $x^{3} +3x^{2} -25x-75$ .

(x-1) - No
(x-3) - No
(x+3) - Yes
(x-5) - Yes
(x+5) - Yes

<u>Step-by-step explanation:</u>

The given equation is f(x)= $x^{3} +3x^{2} -25x-75$ .

Add 0 at the end of the equation.

$x^{3} +3x^{2} -25x-75$ = 0.

Let us group the given equation,

$(x^{3} +3x^{2}) -(25x-75)$ =0.

⇒ Group 1: $x^{3} +3x^{2}$ .

Group 2: $- 25x +75$ .

Pull out factor from each group,

⇒ Group 1: $(x+3)(x^{2})$ .

Group 2: (x+3) (-25).

Join the two group since both (x+3) is common in both groups.

$(x+3)(x^{2} -25)$ =0.

One of the factor is (x+3).

Other factors are solved by the formula, $a^{2}-b^{2} = (a+b) (a-b)$ .

$(x+3)(x^{2} -25)$ = (x+5) (x-5) .

The other factors are (x+5) and (x-5).

7 0

3 years ago

GEOMETRY <br> please Help

geniusboy [140]

Answer:

A right circular cone

Step-by-step explanation:

7 0

3 years ago