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3 years ago

What is the volume of the oblique cube

Mathematics

1 answer:

serious [3.7K]3 years ago

6 0

Answer:

$\large\boxed{V=\dfrac{1600\pi}{3}\ cm^3}$

Step-by-step explanation:

The formula of a volume of a cone:

$V=\dfrac{1}{3}\pi r^2H$

r - radius

H - height

We have r = 10cm and H = 16cm. Substitute:

$V=\dfrac{1}{3}\pi(10^2)(16)=\dfrac{1}{3}\pi(100)(16)=\dfrac{1600\pi}{3}\ cm^3$

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3) Postcards: Marcie wants to make a box to hold her postcard collection from a piece of

klasskru [66]

The volume of the box is the amount of space in it.

The dimension of the postcard is:

$\mathbf{Length = 10}$

$\mathbf{Width = 18}$

Let x represents the length of the cut.

So, the dimension of the box is:

$\mathbf{Length = 10 -2x}$

$\mathbf{Width = 18 -2x}$

$\mathbf{Height = x}$

(a) The function that represents the volume of the box

This is calculated as:

$\mathbf{V(x) = Length \times Width \times Height}$

So, we have:

$\mathbf{V(x) = (10 - 2x) \times (18 - 2x) \times x}$

Expand

$\mathbf{V(x) = 180x - 56x^2 + 4x^3}$

Hence, the volume function is: $\mathbf{V(x) = 180x - 56x^2 + 4x^3}$

(b) The dimension that maximizes the volume

We have:

$\mathbf{V(x) = 180x - 56x^2 + 4x^3}$

Differentiate

$\mathbf{V'(x) = 180- 112x + 12x^2}$

Set to 0

$\mathbf{180- 112x + 12x^2 = 0}$

Using a calculator, we have:

$\mathbf{x = 7.3,2.1}$

The value x = 7.3 is greater than the dimension of the box.

So, we have:

$\mathbf{x = 2.1}$

Recall that:

$\mathbf{Length = 10 -2x}$

$\mathbf{Width = 18 -2x}$

$\mathbf{Height = x}$

So, we have:

$\mathbf{Length = 10 -2 \times 2.1 = 5.8}$

$\mathbf{Width = 18 -2 \times 2.1 = 13.8}$

$\mathbf{Height = 2.1}$

Hence, the dimension that maximizes the volume is 5.8 by 13.8 by 2.1

(c) The maximum volume

This is calculated as the product of the dimension of the box

So, we have:

$\mathbf{Volume = 5.8 \times 13.8 \times 2.1}$

$\mathbf{Volume = 168.1}$

Hence, the maximum volume of the box is 168.1 cubic inches

Read more about volumes at:

brainly.com/question/17056191

5 0

3 years ago

According to a medical study, 15% of people will experience an adverse side effect

ahrayia [7]

Answer:

Step-by-step explanation: trust me

6 0

3 years ago

Read 2 more answers

Let C = {n ∈ Z | n = 6r – 5 for some integer r} and D = {m ∈ Z | m = 3s + 1 for some integer s}.

noname [10]

Its is true that C ⊆ D means Every element of C is present in D

According to he question,

Let C = {n ∈ Z | n = 6r – 5 for some integer r}

D = {m ∈ Z | m = 3s + 1 for some integer s}

We have to prove : C ⊆ D

Proof : Let n ∈ C

Then there exists an integer r such that:

n = 6r - 5

Since -5 = -6 + 1

=> n = 6r - 6 + 1

Using distributive property,

=> n = 3(2r - 2) +1

Since , 2 and r are the integers , their product 2r is also an integer and the difference 2r - 2 is also an integer then

Let s = 2r - 2

Then, m = 3r + 1 with r some integer and thus m ∈ D

Since , every element of C is also an element of D

Hence , C ⊆ D proved !

Similarly, you have to prove D ⊆ C

To know more about integers here

brainly.com/question/15276410

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7 0

2 years ago

148,305 how many hundred

Simora [160]

The places of the digits are ordered as follows (from right to left): units, tens, hundreds, thousands, ten thousands, hundred thousands.
so, in you expression:
5 represents the units
0 represents the tens
3 represents the hundreds
8 represents the thousands
4 represents the ten thousands
1 represents the hundred thousands.

so, the answer for your question is:
there are 3 hundreds

6 0

3 years ago

Plz, help asap!!!!!!

Lorico [155]

Answer:

the answer is 76°

4 0

3 years ago

Read 2 more answers