All categories

3 years ago

Find the volume of the figure: a cube with sides of length s with the biggest sphere that fits in it cut out.

Mathematics

1 answer:

garik1379 [7]3 years ago

6 0

Answer:

Volume of cube= a^3

=(2/√3)^3

=8/3√3 cubic units. (~1.5396 cubic units)

Step-by-step explanation:

Such a cube has diagonal lengths (DF, AG, EC & HB)=diameter of sphere=2 units.

Let the sides of the cube (FG, GC, CB, BF, etc.) be 'a'.

Hence facial diagonal of the cube (FC, BG, FH, etc.) will be √2a (Pythagoras' Theorem).

Applying Pythagoras' theorem for △DFC:

FC²+DC²=FD²

⇒(√2a)²+a²=2²

⇒3a²=4

⇒a=2/√3 units

You might be interested in

<img src="https://tex.z-dn.net/?f=%5Cfrac%7B%281-x%5E%7B2%7D%29%5E%7B%5Cfrac%7B1%7D%7B2%7D%7D%20-x%5E%7B2%7D%20%281-x%5E%7B2%7D%

3241004551 [841]

Step-by-step explanation:

Hi, Hope this will help:)

6 0

3 years ago

A rectangular prism has dimensions of 2 ft, 4 ft, and 6 ft. If the dimensions are doubled, what would happen to the volume?

kondor19780726 [428]

Answer:

Volume is increased in a factor of 8. The volume is increased from $48\,ft^{3}$ to $384\,ft^{3}$ .

Step-by-step explanation:

The formula for the volume of the rectangular prism is:

$V = w\cdot h \cdot l$

Where:

$w$ - Width

$h$ - Height

$l$ - Length

If dimensions are doubled, then volume is increased in a factor of 8:

$V_{f} = (2\cdot w)\cdot (2\cdot h)\cdot (2\cdot l)$

$V_{f} = 8\cdot w \cdot h \cdot l$

$V_{f} = 8 \cdot V_{o}$

The volume is increased from $48\,ft^{3}$ to $384\,ft^{3}$ .

3 0

3 years ago

review the following derivation of the tangent double angle identity. the steps are not listed in the correct order. what is the

poizon [28]

The correct order of the steps used to derive the identity is a. 4,3,5,1,2.

Really talking, identification is a combination of your physical and behavioral traits that define who you are. for example, your call is part of your identity, as is the shape and color of your eyes and your fingerprint. This set of characteristics lets you be definitively and uniquely recognizable.

Identification formation and evolution are impacted by a selection of inner and external elements like society, family, cherished ones, ethnicity, race, subculture, location, possibilities, media, hobbies, looks, self-expression, and lifestyle experiences.

The quick solution is that no, you can not absolutely erase your identity in this day and age -- except the government does it for you. Legally changing your call is not too hard. Legally converting your Social protection number (SSN) is feasible as nicely, but only below positive instances.

Learn more about identity here brainly.com/question/24496175

#SPJ4

8 0

2 years ago

A hockey player strikes a hockey puck. The height of the puck increases until it reaches a maximum height of 3 feet, 55 feet awa

MariettaO [177]

Answer:

The maximum height of the second pluck is greater than that of the first pluck, hence the second pluck travels further

Also the distance of the maximum height of first pluck from the player is less than the distance of the second pluck from the player hence the second pluck travels further

Step-by-step explanation:

From the question we are told that

The maximum height of the first pluck is $h_1 = 3 \ ft$

The height of the second height is mathematically represented as

$$y=x\left(0.15-0.001x\right)$

=> $y=0.15x -0.001x^2$

Generally at maximum height $y' = 0$

$y'=0.15 -0.002 x = 0$

=> $x = 75 \ ft$

Here 75 ft is the horizontal distance the second pluck traveled at maximum height

So the maximum height of the second pluck is mathematically represented as

$y=0.15(75) -0.001(75)^2$

=> $y= 5.625 \ ft$

So comparing the maximum height of the first and the second pluck we see that the maximum height of the second pluck is greater than that of the first pluck, hence the second pluck travels father

3 0

3 years ago

Input(x) Output(y)

Fiesta28 [93]

Answer:

Rule : x subtracted by 12 = y , first ? = 6 (6,-6) , second ? = -22 (-10,-22)

4 0

3 years ago