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3 years ago

What base side length does the rectangular prism need to have the same volume??????

Mathematics

1 answer:

valkas [14]3 years ago

7 0

Because you know that both the rectangular prism and the rectangular prism have the same volume, you can divide 588 cm^3 by 12cm to find the area of the base and get 49 cm^2. The base of the rectangular prism is x^2 so to solve just find the square rootof 49 cm^2 to get the side lengths (7 cm).

Hope this helped

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Luden [163]

Cone details:

height: h cm

radius: r cm

Sphere details:

radius: 10 cm

================

From the endpoints (EO, UO) of the circle to the center of the circle (O), the radius is will be always the same.

Using Pythagoras Theorem

(a)

TO² + TU² = OU²

(h-10)² + r² = 10² [insert values]

r² = 10² - (h-10)² [change sides]

r² = 100 - (h² -20h + 100) [expand]

r² = 100 - h² + 20h -100 [simplify]

r² = 20h - h² [shown]

r = √20h - h² ["r" in terms of "h"]

(b)

volume of cone = 1/3 * π * r² * h

===========================

$\longrightarrow \sf V = \dfrac{1}{3} * \pi * (\sqrt{20h - h^2})^2 \ ( h)$

$\longrightarrow \sf V = \dfrac{1}{3} * \pi * (20h - h^2) (h)$

$\longrightarrow \sf V = \dfrac{1}{3} * \pi * (20 - h) (h) ( h)$

$\longrightarrow \sf V = \dfrac{1}{3} \pi h^2(20-h)$

To find maximum/minimum, we have to find first derivative.

(c)

First derivative

$\Longrightarrow \sf V' =\dfrac{d}{dx} ( \dfrac{1}{3} \pi h^2(20-h) )$

apply chain rule

$\sf \Longrightarrow V'=\dfrac{\pi \left(40h-3h^2\right)}{3}$

Equate the first derivative to zero, that is V'(x) = 0

$\Longrightarrow \sf \dfrac{\pi \left(40h-3h^2\right)}{3}=0$

$\Longrightarrow \sf 40h-3h^2=0$

$\Longrightarrow \sf h(40-3h)=0$

$\Longrightarrow \sf h=0, \ 40-3h=0$

$\Longrightarrow \sf h=0,\:h=\dfrac{40}{3}$

maximum volume: when h = 40/3

$\sf \Longrightarrow max= \dfrac{1}{3} \pi (\dfrac{40}{3} )^2(20-\dfrac{40}{3} )$

$\sf \Longrightarrow maximum= 1241.123 \ cm^3$

minimum volume: when h = 0

$\sf \Longrightarrow min= \dfrac{1}{3} \pi (0)^2(20-0)$

$\sf \Longrightarrow minimum=0 \ cm^3$

6 0

2 years ago

Read 2 more answers

Is -0.025 greater or less than -0.14?

AlekseyPX

Answer:

less than

Step-by-step explanation:

-0.025 is further away from -0.14 in the number line.

8 0

3 years ago

n a survey, 480 people, or 75%, said they attended a movie at least once a month. How many people were surveyed

scoundrel [369]

Answer:

640 people

Explanation:

480 people = 75 %
x people = 100%

480 : x = 75 : 100
75 x = 48,000
x = 48,000 : 75
x = 640

5 0

3 years ago

Read 2 more answers

HELP HELP PLEASE IMPORTANT

Yuliya22 [10]

Answer:

2010

Step-by-step explanation:

1/2(24)(20)=240

50*45=2250

2250-240=2010

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3 years ago

A tennis ball is 2 inch in diameter. How many tennis ball will fill a room of 20ft by 16ft by 18ft if no space wasted?

krek1111 [17]

The number of tennis ball that will fill the room is 1,371 tennis balls.

Given:

Diameter of ball (d) : 2 inch

Radius (r) = half of diameter = 1 inch

Dimension of room = 20ft by 16ft by 18ft

Number of balls that will fill the room = Volume of each ball/volume of the room

Volume of the ball = volume of a sphere = $\frac{4}{3} \pi r^{3}$

Where,

r = 1

let $\pi = 3.14$

Substitute:

$Volume = \frac{4}{3} \times 3.14 \times 1^{3} \\Volume = 4.2in^{3}$

Volume of the room = $20 \times 16 \times 18 \\$

$= 5,760$

Therefore:

number of tennis balls that will fill the room = $\frac{5,760}{4.2} = 1,371.4$

Therefore, the number of tennis ball that will fil the room will be approximately 1,371.

Learn more about volume here:

brainly.com/question/16098833

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2 years ago