Tower

The top of the tower is a regular hexagonal pyramid with base edge 8 meters long and a height 5 meters. How many m² of the sheet is required to cover the top of the tower if we count 8% of the sheet waste?

Result

S =  221 m²

Solution:

$\ \\ a = 8 \ m \ \\ v = 5 \ m \ \\ \ \\ a^2-(a/2)^2 = v_2^2 \ \\ v_2 = a \dfrac{ \sqrt3}{2} = 6.928\ m \ \\ \ \\ h^2 = v^2+v_2^2 \ \\ h = \sqrt{ 5^2 + 6.928^2 } = 8.544 \ m \ \\ \ \\ S_1 = \dfrac12 a h = \dfrac12 \cdot 8 \cdot 8.544 = 34.18 \ m^2 \ \\ \ \\ S = 6 \cdot S_1 \cdot (1+\dfrac{ 8}{100}) = 6 \cdot 34.18 \cdot 1.08 = 221 \ m^2$

Try another example

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

Showing 0 comments:

Be the first to comment!

Next similar math problems:

1. Church roof
   The roof of the church tower has the shape of a regular tetrahedral pyramid with base edge length 5.4 meters and a height 5 m. It was found that needs to be corrected 27% covering of the roof area. What amount of material will be required?
2. Roof 7
   The roof has the shape of a regular quadrangular pyramid with a base edge of 12 m and a height of 4 m. How many percent is folds and waste if in construction was consumed 181.4m2 of plate?
3. House roof
   The roof of the house has the shape of a regular quadrangular pyramid with a base edge 17 m. How many m² is needed to cover roof if roof pitch is 57° and we calculate 11% of waste, connections and overlapping of area roof?
4. Tetrahedral pyramid
   What is the surface of a regular tetrahedral (four-sided) pyramid if the base edge a=16 and height v=16?
5. Hexagon
   There is regular hexagon ABCDEF. If area of the triangle ABC is 22, what is area of the hexagon ABCDEF? I do not know how to solve it simply....
6. Tent
   Pyramid-shaped tent has a base square with a side length of 2 m and a height 1.7 m. How many meters of canvas is nneded to make it if for a waste should be added 10%?
7. Right angled
   From the right triangle with legs 12 cm and 20 cm we built a square with the same content as the triangle. How long will be side of the square?
8. The farmer
   The farmer would like to first seed his small field. The required amount depends on the seed area. Field has a triangular shape. The farmer had fenced field, so he knows the lengths of the sides: 119, 111 and 90 meters. Find a suitable way to determine t
9. Borrowing
   I borrow 25,000 to 6.9% p.a.. I pay 500 per month. How much will I pay and for how long?
10. Profit gain
    If 5% more is gained by selling an article for Rs. 350 than by selling it for Rs. 340, the cost of the article is:
11. 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?
12. Calculation
    How much is sum of square root of six and the square root of 225?
13. Summerjob
    The temporary workers planted new trees. Of the total number of 500 seedlings, they managed to plant 426. How many percents did they meet the daily planting limit?
14. Triangle
    The triangle has known all three sides: a=5.5 m, b=5.3 m, c= 7.8 m. Calculate area of ​this triangle.
15. Diameters of circles
    How many percent of the area of a larger circle is a smaller circle if the smaller circle has a diameter 120 mm and a larger one has a diameter 300 mm?
16. Percentage increase
    Increase number 400 by 3.5%
17. Power
    Number ?. Find the value of x.