All categories

3 years ago

Find the volume of the figure: a prism of volume 15 with a pyramid of the same height cut out.

Mathematics

1 answer:

SashulF [63]3 years ago

7 0

The volume of the figure is 10 cubic units, if a prism of volume 15 with a pyramid of the same height cut out.

Step-by-step explanation:

The given is,

A prism of volume 15

A pyramid of the same height cut out

For the above question diagram is missing, so i attach the diagram.

Step:1

Ref the attachment,

Volume of figure = Volume of Prism - Volume of Pyramid....(1)

Step:2

From the given diagram,

Formula for volume of prism,

$V_{prism} = whl$ ......................(2)

Where, w - Width of the prism

h - Height of prism

l - Length of prism

From the given,

Volume, V = 15 cubic units

l = a

w = b

h = c

Equation (1) becomes,

15 = abc

c = $\frac{15}{ab}$

Step:3

Volume of pyramid, $V = \frac{whl}{3}$ ..........................(2)

where,

w - Width of pyramid

h - Height of pyramid

l - Length of pyramid

From the given,

l = a

w = b

h = c

From the volume of prism, h = c = $\frac{15}{ab}$

Equation (2) becomes,

$V_{pyramid} = (\frac{ab}{3} )(\frac{15}{ab } )$

= 5

$V_{pyramid} = 5$ cubic units

Step:4

Equation (1) becomes,

Volume of figure = 15 - 5

= 10 cubic units

Result:

The volume of the figure is 10 cubic units, if a prism of volume 15 with a pyramid of the same height cut out.

You might be interested in

Please help me asap i will give brainiest and all my points

Alinara [238K]

Answer:

a. Not Divisible

b. Divisible

c. Divisible

d. Divisible

e. Divisible

Step-by-step explanation:

To find the divisibility we need to follow the PEMDAS rule and check if the total value can be divided by the selected numbers without returning a remainder.

Let's begin with a:

$16^{5}+215$ by 33

$1,048,576 + 215$

$1,048,791$

We now then divide the total amount with 33.

$\dfrac{1,048,576}{33}$

= 31,781.5454

We can see that the value has a decimal point indicating that the total value divided by 33 will return a remainder. So it is NOT Divisible by 33.

Now let's continue on with the others.

$51^{7}-51^{6}$ by 25

$897,410,677,851 - 17,596,287,801$

$879,814,390,050$

We now then divide the total amount with 25.

$\dfrac{879,814,390,050}{25}$

= 35,192,575,602

The total value did NOT return a decimal point, therefore making the equation true. $51^{7}-51^{6}$ IS divisible by 25.

Next on we have:

$5^{5}-5^{4} +5^{3}$ by 7

$3,125 - 625 + 125$

As we know in the PEMDAS rule, that addition comes first. In this situation we have to read the equation from left to right and solve which ever comes first.

$2,500 + 125$

$2,625$

We now then divide the total amount with 7.

$\dfrac{2,625}{7}$

= 375

The total value did NOT return a decimal point, therefore making the equation true. $5^{5}-5^{4} +5^{3}$ IS divisible by 7.

$7^6+7^5-7^4$ by 11

$117,649+16,807-2,401$

$134,456-2,401$

$132,055$

We now then divide the total amount with 11.

$\dfrac{132,055}{11}$

= 12,005

The total value did NOT return a decimal point, therefore making the equation true. $7^6+7^5-7^4$ IS divisible by 11.

Last but not the least:

$5^{23}-5^{21}$ by 24

$11,920,928,955,078,125-476,837,158,203,125$

$11,444,091,796,875,000$

We now then divide the total amount with 24.

$\dfrac{11,444,091,796,875,000}{24}$

= 476,837,158,203,125

The total value did NOT return a decimal point, therefore making the equation true. $5^{23}-5^{21}$ IS divisible by 24.

5 0

3 years ago

The stock of Company A lost $4.17 throughout the day and ended at a value of

Anit [1.1K]

Answer:

Step-by-step explanation:

After losing 4.17, it came down to 100.08, so the opening price was:

100.08 + 4.17 = 104.25

To find percentage decline, we find the ratio of the "change" (which is 4.17) divided by the opening (original) price, which is 104.25. Then we multiply that fraction by 100 to get our percentage decline.

So,

$\frac{4.17}{104.25}*100=4$

Thus, the

percentage decline = 4%

4 0

3 years ago

Julia has 2 identical rooms in her house. if each room measures 8 feet on one side and 12 feet on another, what is the total are

Jlenok [28]

First we have the work out the area of 1 room. So that is 8ft * 12ft which is 96ft^2. And if there are 2 of these rooms, then we multiply this value by 2. Giving us a total area of 192ft^2.

5 0

4 years ago

What is 2 times 2 and 7/8

anyanavicka [17]

2 x 2 7/8 = 5 3/4 hope it helps

6 0

4 years ago

Read 2 more answers

what is the volume of a cone with a diameter of 30 feet and height of 60 feet? use 3.14 for pi. enter your answer in the box

Marizza181 [45]

The volume of a cone with a diameter of 30 feet and a height of 60 feet is 14130.

<h3>What is the volume of a cone?</h3>