# Heptagonal pyramid

A hardwood for a column is in the form of a frustum of a regular heptagonal pyramid. The lower base edge is 18 cm and the upper base of 14 cm. The altitude is 30 cm. Determine the weight in kg if the density of the wood is 10 grams/cm3.

Result

m =  17.397 kg

#### Solution:

$s_{ 1 } = 18 \ cm \ \\ s_{ 2 } = 14 \ cm \ \\ h = 30 \ cm \ \\ \ \\ \ \\ n = 7 \ \\ \ \\ S_{ 1 } = \dfrac{ 1 }{ 4 } \cdot \ n \cdot \ s_{ 1 } \cdot \ \cotg(\pi/n) = \dfrac{ 1 }{ 4 } \cdot \ 7 \cdot \ 18 \cdot \ \cotg(3.1416/7) \doteq 65.4104 \ cm^2 \ \\ S_{ 2 } = \dfrac{ 1 }{ 4 } \cdot \ n \cdot \ s_{ 2 } \cdot \ \cotg(\pi/n) = \dfrac{ 1 }{ 4 } \cdot \ 7 \cdot \ 14 \cdot \ \cotg(3.1416/7) \doteq 50.8748 \ cm^2 \ \\ \ \\ V = \dfrac{ 1 }{ 3 } \cdot \ h \cdot \ ( S_{ 1 }+S_{ 2 } + \sqrt{ S_{ 1 } \cdot \ S_{ 2 } }) = \dfrac{ 1 }{ 3 } \cdot \ 30 \cdot \ ( 65.4104+50.8748 + \sqrt{ 65.4104 \cdot \ 50.8748 }) \doteq 1739.7177 \ cm^3 \ \\ \ \\ \ \\ ρ = 10 \ g/cm^3 \ \\ \ \\ m_{ 1 } = ρ \cdot \ V = 10 \cdot \ 1739.7177 \doteq 17397.177 \ g \ \\ \ \\ m = m_{ 1 } \rightarrow kg = m_{ 1 } / 1000 \ kg = 17.3971769886 \ kg = 17.397 \ \text { kg }$

Our examples were largely sent or created by pupils and students themselves. Therefore, we would be pleased if you could send us any errors you found, spelling mistakes, or rephasing the example. Thank you!

Leave us a comment of this math problem and its solution (i.e. if it is still somewhat unclear...):

Be the first to comment!

#### Following knowledge from mathematics are needed to solve this word math problem:

Looking for a statistical calculator? Do you know the volume and unit volume, and want to convert volume units? Tip: Our Density units converter will help you with the conversion of density units. Do you want to convert mass units?

## Next similar math problems:

1. Roof 8
How many liters of air are under the roof of tower which has the shape of a regular six-sided pyramid with a 3,6-meter-long bottom edge and a 2,5-meter height? Calculate the supporting columns occupy about 7% of the volume under the roof.
2. Theorem prove
We want to prove the sentence: If the natural number n is divisible by six, then n is divisible by three. From what assumption we started?
3. Vegan shop
To the shops brought together 23.2 kg of goods, fruits, vegetables and nuts. fruit was 4.7 kg more than vegetables, nuts was 1.5 kg less than the fruit. Determine the amount of fruits, vegetables and nuts.
4. Three friends
Danica, Lenka and Dalibor have altogether 96 kg. Lenka weighs 75% more than Dalibor and Danica weighs 6 kg more than Dalibor. Determine the weight of Danice, Lenka and Dalibor.
5. Solid in water
The solid weighs in air 11.8 g and in water 10 g. Calculate the density of the solid.
6. Bottles
The must is sold in 5-liter and 2-liter bottles. Mr Kucera bought a total of 216 liters in 60 bottles. How many liters did Mr. Kucera buy in five-liter bottles?
7. Trio weight
Adelka, Barunka, and Cecilka are weight in pairs. Adelka with Barunka weighs 98 kg, Barunka with Cecilka 90 kg and Adelka with Cecilka 92 kg. How much does each of them weigh?
8. Potatoes
For three days the store sold 1400 kg of potatoes. The first day they sold 100 kilograms of potatoes less than the second day, the third-day three-fifths of what they sold the first day. How many kgs of potatoes sold every day?
9. Blocks
There are 9 interactive basic building blocks of an organization. How many two-blocks combinations are there?
10. PIN - codes
How many five-digit PIN - code can we create using the even numbers?
11. Insect spraying
In 600 ml of spraying is 5 ml of an active ingredient. How much is it per miles?
12. Legs
Cancer has 5 pairs of legs. The insect has 6 legs. 60 animals have a total of 500 legs. How much more are cancers than insects?
13. Elimination method
Solve system of linear equations by elimination method: 5/2x + 3/5y= 4/15 1/2x + 2/5y= 2/15
14. Line
It is true that the lines that do not intersect are parallel?
15. Reference angle
Find the reference angle of each angle:
16. AP - simple
Determine the first nine elements of sequence if a10 = -1 and d = 4
17. Today in school
There are 9 girls and 11 boys in the class today. What is the probability that Suzan will go to the board today?