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maksim [4K]
2 years ago
11

Question content area top

Mathematics
1 answer:
BigorU [14]2 years ago
3 0

The volume of the slice is 40 in³. The volume of the remaining cake would be 197.014 in³.

<h3>What is a regular hexagon?</h3>

A regular hexagon can be defined as a closed shape consisting of six equal sides and six equal angles.

Here we have two regular hexagons

one top small hexagon cake with a side of length = 3 in, height = 3 in

One big hexagon cake, side of length = 4 in, Height = 4 in

A slice cut such that it removes a side segment is equivalent to an equilateral triangle with a side

length = length of hexagon side

The length of the side of the removed equilateral triangle side

Top small cake slice triangle side = 3 in.

Area of surface of small slice = 1/2 x b x h = 1/2 x 3 x 3 x sin 60

                                                = 9√3/ 4

The volume of a small slice  

=  Area of surface small slice × Height of small cake

= 9√3/ 4  x 3

= 11. 69

Big cake slice triangle side = 4 in.

Area of the surface of big slice = 1/2 x 4 x 4 x sin 60

                                                    = 4√3

The volume of big slice =  Area of the surface of big slice × Height of big slice

= 16√3

= 28

The total volume of slice = Volume of small slice + Volume of big slice

Total volume of slice = 12 in³ +28 in³ = 40 in³

For the small cake,

the remaining volume = 5 x 11.69 = 58.45

For the big cake

the remaining volume = 5 x 27.71 = 138.56

Total volume remaining cake

= 58.45 in³ + 138.56 in³ = 197.014 in³

a = Length of side

h = Height of hexagon

The volume of each slice is,

= a^2 x h x √3/4

For the small cake, we have

a = 3 in.

h = 3 in.

The volume of small slice = a^2 x h x √3/4

                                   = 9 x 3 x √3/4

                                   = 27√3/4

For the big cake, we have

a = 4 in.

h = 4 in.

Volume of big slice =  a^2 x h x √3/4

                                = 16 √3

The total volume of slice = Volume of small slice + Volume of a big slice

Total volume of slice = 27√3/4 + 16 √3

The total volume of the slice = 39404 in³.

Learn more about hexagon;

brainly.com/question/16025389

#SPJ1

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Less than because !2.56 bascically means just 12 and 125.6 means bascally just 125 and 125 is waay more than 12
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3 years ago
This the questions that have me stuck​
IRINA_888 [86]
First a and then b.
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3 years ago
please help. will give brainliest! review the table of values for function p(x). what is lim (x -14) p(x), if it exists? (table
Lubov Fominskaja [6]

Answer:

DNE

Step-by-step explanation:

The the given table, we have;

As x approaches -14 from the left, at x = -14.001,  p(x) = 1.96

\lim \limits _{x \to -14^{-}} p(x) = 1.96

As x approaches -14 from the right, at x = -13.999, p(x) = 1.97

\lim \limits _{x \to -14^{+}} p(x) = 1.97

The value of p(x) when x = -14 is \lim \limits _{x \to -14} p(x) = Undefined, or is not definable, therefore, p(x) Does Not Exist (DNE) when x = -14, and we have;

\lim \limits _{x \to -14} p(x)  Does Not Exist, DNE.

3 0
3 years ago
Rectangular prism A measures 2 inches by 7 inches by 8 inches. Rectangular prism B measures 1 inches by 5 inches by 10 inches.
satela [25.4K]

The Volume for Rectangular prism A is 172 inches², Volume = 112 inches³

Surface Area to Volume Ratio = 43/28

<h3>Mensuration of Solids</h3>

Given Data

Rectangular prism A

Length = 2 inches

Width = 7 inches

Height = 8 inches

Surface Area

A=2(wl+hl+hw)

A=2(7*2+8*2+8*7)

A=2(14+16+56)

A= 172 inches²

Volume

Volume = L*W*H

Volume = 2*7*8

Volume = 112 inches³

Surface Area to Volume Ratio

= 172/112

= 43/28

Learn more about Mensuration of Solids here:

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2 years ago
Write the equation for the function graphed attached <br><br> f(x)=
Anna007 [38]

Answer:

here

Step-by-step explanation:

7 0
2 years ago
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