# 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.

Correct result:

m =  17.397 kg

#### Solution:

$s_{1}=18 \ \text{cm} \ \\ s_{2}=14 \ \text{cm} \ \\ h=30 \ \text{cm} \ \\ \ \\ \ \\ n=7 \ \\ \ \\ S_{1}=\dfrac{ 1 }{ 4 } \cdot \ n \cdot \ s_{1} \cdot \ \cotg(\pi/n)=\dfrac{ 1 }{ 4 } \cdot \ 7 \cdot \ 18 \cdot \ \cotg(3.1416/7) \doteq 65.4104 \ \text{cm}^2 \ \\ S_{2}=\dfrac{ 1 }{ 4 } \cdot \ n \cdot \ s_{2} \cdot \ \cotg(\pi/n)=\dfrac{ 1 }{ 4 } \cdot \ 7 \cdot \ 14 \cdot \ \cotg(3.1416/7) \doteq 50.8748 \ \text{cm}^2 \ \\ \ \\ V=\dfrac{ 1 }{ 3 } \cdot \ h \cdot \ ( S_{1}+S_{2} + \sqrt{ S_{1} \cdot \ S_{2} })=\dfrac{ 1 }{ 3 } \cdot \ 30 \cdot \ ( 65.4104+50.8748 + \sqrt{ 65.4104 \cdot \ 50.8748 }) \doteq 1739.7177 \ \text{cm}^3 \ \\ \ \\ \ \\ ρ=10 \ \text{g/cm}^3 \ \\ \ \\ m_{1}=ρ \cdot \ V=10 \cdot \ 1739.7177 \doteq 17397.177 \ \text{g} \ \\ \ \\ m=m_{1} \rightarrow kg=m_{1} / 1000 \ kg=17397.1769886 / 1000 \ kg=17.397 \ kg=17.397 \ \text{kg}$

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!

Please write to us with your comment on the math problem or ask something. Thank you for helping each other - students, teachers, parents, and problem authors.

Tips to related online calculators
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?
Most natural application of trigonometry and trigonometric functions is a calculation of the triangles. Common and less common calculations of different types of triangles offers our triangle calculator. Word trigonometry comes from Greek and literally means triangle calculation.

#### You need to know the following knowledge to solve this word math problem:

We encourage you to watch this tutorial video on this math problem:

## Next similar math problems:

• Between two bus stops
Wanda lives between two bus stops at three-eighths of their distance. He started the house today and found that whether he was running to one or the other stop, he would have arrived at the bus stop. The average bus speed is 60 km/h. What is the average s
• Average speed
The truck drove 1/2 of the way on the highway at 80km/h. The other half of the way 20km/h. Calculate the average speed
• Ball bearings
One bearing is selected from the shipment of ball bearings. It is known from previous deliveries that the inner bearing radius can be considered as a normal distribution of N (µ = 0.400, σ2 = 25.10^−6). Calculate the probability that the selected radius w
• Carpenters
Carpenters 1 and 2 spend 10 days and 5 days respectively to make one table. If 50 tables were made by the first carpenter and 30 tables were made by the second carpenter, What is the average time spent on the products?
• Standard deviation
Find standard deviation for dataset (grouped data): Age (years) No. Of Persons 0-10 15 10-20 15 20-30 23 30-40 22 40-50 25 50-60 10 60-70 5 70-80 10
• US GDP
Consider the following dataset , which contsins the domestic US gross in millions of the top grossing movie over the last 5 years. 300,452,513,550,780 I. Find the Mean of the Dataset II. Find the Squared deviation of the second observation from the mean I
• Controller
Output Controller of the company in the control of 50 randomly selected products found that 37 of them had no defect 8 has only one flaw, three had two defects, and two products had three defects. Determine the standard deviation and coefficient of variat
• SD - mean
Mean is 10 and standard deviation is 3.5. If the data set contains 40 data values, approximately how many of the data values will fall within the range 6.5 to 13.5?
• City market
Apples were sold at contractual prices at the city market. Calculate the average price of 1 kg of apples sold: Stand, Sale kg, Price CZK/kg 1 325 6.20 2 194 7.00 3 258 6.50 4 870 5.90 5 275 6.40
• Lifespan
The lifetime of a light bulb is a random variable with a normal distribution of x = 300 hours, σ = 35 hours. a) What is the probability that a randomly selected light bulb will have a lifespan of more than 320 hours? b) Up to what value of L hours can the
• Average height
There are twice as many girls in the class as there are boys. The average height of girls is 177 cm, boys 186 cm. What is the average height of students in this class?
• Corona virus
Calculate an estimate of the percentage of GDP (Gross Domestic Product) declined due to the quarantine related to the corona COVID-19 virus that lasts for 2 months, during which time the economic activity is down by 80%.
• Mixture of nuts
The mixture of nuts should be prepared from almonds, peanuts and cashew nuts ratio 1: 2: 3 (respectively). The price of almonds is 150 CZK/kg, the price of peanuts is 140 CZK/kg and the price of cashew nuts is 180 CZK/kg. The price of the mixture is deter
• The triangle
The triangle is given by three vertices: A [0.0] B [-4.2] C [-6.0] Calculate V (intersection of heights), T (center of gravity), O - center of a circle circumscribed
• Life expectancy
The life expectancy of batteries has a normal distribution with a mean of 350 minutes and standard deviation of 10 minutes. What the range in minutes 68% of the batteries will last? What is the range in minutes approximately 99.7% of batteries will last?
• Uphill and downhill
The cyclist moves uphill at a constant speed of v1 = 10 km/h. When he reaches the top of the hill, he turns and passes the same track downhill at a speed of v2 = 40 km/h. What is the average speed of a cyclist?
• Centroid - two bodies
A body is composed of a 0.8 m long bar and a sphere with a radius of 0.1m attached so that its center lies on the longitudinal axis of the bar. Both bodies are of the same uniform material. The sphere is twice as heavy as the bar. Find the center of gravi