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2 years ago

A cylinder is inscribed in a cube. If the edge of the cube is 3" long, find the volume of the cylinder.

Mathematics

2 answers:

Mazyrski [523]2 years ago

6 0

Answer:

The volume of cylinder is 21.21 units³.

Step-by-step explanation:

The side length of cube is 3 units.

If a cylinder is inscribed in that cube, then radius of the cylinder is 1.5 units and height of the cylinder is 3 units.

The volume of the cylinder is

$V=\pi r^2h$

The volume of cylinder is

$V=\pi \times (1.5)^2\times (3)$

$V=21.20575$

$V\approx 21.21$

Therefore the volume of cylinder is 21.21 units³.

maks197457 [2]2 years ago

4 0

Answer:

21.2 cubic inches

Step-by-step explanation:

Supposing that the diameter of the cylinder match with the longitude of the edge of the cube (see figure attached); then, cylinder's diameter (D) and height (h) are equal to 3 inches.

The volume of the cylinder (V) is calculated as follows:

V = π*(D^2)/4*h

V = π*(3^2)/4*3

V = 21.2 cubic inches

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Dwayne buys ingredients to make a cake. He buys 1 1/2 pounds of flour, 12 ounces of coconut, and 1 1/4 pounds of sugar. What is

AVprozaik [17]

Answer:

3.05 or 31/2 pounds

56 ounces

Step-by-step explanation:

To find the total weight all the weights have to have the same units of measurements

It is either pounds is converted to ounces or ounces is converted to pounds

1. convert ounces to pound

1 ounce = 0.0625

12 ounces = 0.0625 x 12 = 0.75 pounds or 3/4

add together = 1 1/2 + 3/4 + 1 1/4 = $1\frac{1}{2} + \frac{3}{4} + 1\frac{1}{4}$

$2\frac{2 +3 + 1}{4}$ = $2\frac{6}{4}$ = 3 1/2

2. 16 ounces = 1 pound

flour = 16 x 1 1/2 = 24

sugar = 16 x 1 1/4 = 20

total = 24 + 20 + 12 = 56 ounces

6 0

3 years ago

Use the method of reduction of order to find a second solution to t^2y' + 3ty' – 3y = 0, t> 0 Given yı(t) = t y2(t) = Preview

Anestetic [448]

Let $y_2(t)=tv(t)$ . Then

${y_2}'=tv'+v$

${y_2}''=tv''+2v'$

and substituting these into the ODE gives

$t^2(tv''+2v')+3t(tv'+v)-3tv=0$

$t^3v''+5t^2v'=0$

$tv''+5v'=0$

Let $u(t)=v'(t)$ , so that $u'(t)=v''(t)$ . Then the ODE is linear in $u$ , with

$tu'+5u=0$

Multiply both sides by $t^4$ , so that the left side can be condensed as the derivative of a product:

$t^5u'+5t^4u=(t^5u)'=0$

Integrating both sides and solving for $u(t)$ gives

$t^5u=C\implies u=Ct^{-5}$

Integrate again to solve for $v(t)$ :

$v=C_1t^{-6}+C_2$

and finally, solve for $y_2(t)$ by multiplying both sides by $t$ :

$tv=y_2=C_1t^{-5}+C_2t$

$y_1(t)=t$ already accounts for the $t$ term in this solution, so the other independent solution is $y_2(t)=t^{-5}$ .

6 0

3 years ago

Plss answer Part A #1 abc . i will give brainliest. late answers accepted

kenny6666 [7]

Answer:

a. (3x² - 2x - 5) units²

b. (x² - x) units²

c. (2x² - x - 5) units²

Step-by-step explanation:

a. Area of the frame = L*W

L = (x + 1) units

W = (3x - 5) units

Area of the frame = (x + 1)(3x - 5)

Apply distributive property

x(3x - 5) +1(3x - 5)

3x² - 5x + 3x - 5

Area of the frame = (3x² - 2x - 5) units²

b. Area of the picture = L*W

L = x units

W = (x - 1) units

Area of the picture = x(x - 1)

Apply distributive property

= x² - x

Area of picture = (x² - x) units²

c. Area of the frame that surrounds the picture = area of frame - area of picture

= (3x² - 2x - 5) - (x² - x)

= 3x² - 2x - 5 - x² + x (distributive property)

Add like terms

= 3x² - x² - 2x + x - 5

= 2x² - x - 5

Area of the frame that surrounds the picture = (2x² - x - 5) units²

4 0

2 years ago

Trevor gets paid to 1250 per month plus a commission of 5% of his monthly sells his sales at the end of this month are 10350 how

Mama L [17]

Answer:

$1767.5

Step-by-step explanation:

Trevor gets paid $1250 plus a comission of 5% of his onthly sells.

His monthly sales is $10350, therefore the comission is: $10350×0.05 = $517.5

Therefore, his total pay for the month is: $1250 + $517.5 = $1767.5

3 0

3 years ago

How do I find x and y?

Lelechka [254]

2y = x + y (Vertically opposite ∠s)
2y - y = x
y = x

∴3x = 180°
x = y = 60°

X + y = 60° + 60° = 120°

8 0

3 years ago