6 The manufacturer of an oven states that the

Mathematics

1 answer:

Len [333]3 years ago

7 0

Result, Rachel can be certain that the temperature is suitable for her cake.

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Find the volume of a regular hexahedron if one of the diagonals of its faces is 8 root 2 inches.

Naily [24]

The answer is 114sqrt{6} in³

A regular hexahedron is actually a cube.

Diagonal of a cube D is a hypotenuse of a right triangle which other two legs are face diagonal (f) and length of a side (a):
D² = f² + a²

Face diagonal is a hypotenuse of a right triangle which sides are a and a:
f² = a² + a² =2a²

D² = f² + a²
f² = 2a²

D² = 2a² + a² = 3a²
D = √3a² = √3 * √a² = √3 * a = a√3

Volume of a cube with side a is: V = a³
D = a√3
⇒ a = D/√3

V = a³ = (D/√3)³

We have:
D = 8√2 in

$V= (\frac{D}{ \sqrt{3} } )^{3} =( \frac{8 \sqrt{2} }{ \sqrt{3} } )^{3}=( \frac{8 \sqrt{2} * \sqrt{3} }{ \sqrt{3}* \sqrt{3}} )^{3} =( \frac{8 \sqrt{2*3} }{ \sqrt{3*3}} )^{3} =( \frac{8 \sqrt{6} }{ \sqrt{3^{2} }} )^{3} =( \frac{8 \sqrt{6} }{ 3} )^{3} = \\ \\ = \frac{ 8^{3} *( \sqrt{6} )^{3}}{3^{3}} = \frac{512* \sqrt{6 ^{2} }* \sqrt{6} }{27} = \frac{512*6* \sqrt{6} }{27} = 114sqrt{6}$

8 0

3 years ago

Suppose one bag contains 500 cubic inches of confetti. How many bags will Student Government need to fill 100 containers? If the

Vanyuwa [196]

The number of bags that they will need if each bag contains 500 cubic inches of confetti is 20,000

<h3>How to find the total volume ?</h3>

One bag contains 500 cubic inches of confetti.

Therefore,

1 bag = 500 inches³

The student need to fill 100 containers with the bag.

Each container can accomodates 100,000 cubic inches.

Therefore,

1 bag = 500 inches³

100,000inches³ = 1 container = 200 bags

Therefore,

100 containers will contain 20, 000 bags of confetti.

learn more on volume here: brainly.com/question/10224096

5 0

2 years ago

Plz helllppp.. Ill mark as brainliest to who hepls. :3 ThankU m8

julia-pushkina [17]

First do ,60 divided by 7 =_____. Then do The product of that equation divided by 8. Then ur answer to that equation is a factor for the last equation u have to do witch is The product of ______ divided by 8, Then multiple that product by 3 like this (3❌_______=_______) then u have ur answer. Hope u understand more now that I've helped

5 0

3 years ago

Read 2 more answers

State the domain and range<br> {(2,4), (3,7), (4,9), (6,11)}

mihalych1998 [28]

Answer:

Domain= 2,3,4,6

Range=4,7,9,11

Domain [2,6]

Range [4,11]

Step-by-step explanation:

3 0