How many

How many m² of copper sheet is needed to replace the roof of a conical tower with a diameter of 13 meters and a height of 24 meters, if we count 8% of the material for bending and waste?

Correct result:

S =  548.3641 m²

Solution:

$$\begin{gathered} D=13\text{ m } \\ h=24\text{ m } \\ q=8\mathrm{\%}=1+{\displaystyle \frac{8}{100}}=1.08 \\ r=D\mathrm{/}2=13\mathrm{/}2={\displaystyle \frac{13}{2}}=6.5\text{ m } \\ s=\sqrt{h^2+r^2}=\sqrt{24^2+6.5^2}\doteq 24.8646\text{ m } \\ {S}_1=\pi \cdot r\cdot s=3.1416\cdot 6.5\cdot 24.8646\doteq 507.7446{\text{m}}^2 \\ S=q\cdot S_1=1.08\cdot 507.7446=548.3641{\text{m}}^2 \end{gathered}$$

Try another example

Showing 0 comments:

Next similar math problems:

• Castle tower
  The castle tower has a cone-shaped roof with a diameter of 10 meters and a height of 8 meters. Calculate how much m² of coverage is needed to cover it if we must add one-third for the overlap.
• Tower
  How many m² of copper plate should be to replace roof of the tower conical shape with diameter 24 m and the angle at the vertex of the axial section is 144°?
• Roof cover
  Above the pavilion with a square ground plan with a side length of a = 12 m is a pyramid-shaped roof with a height v = 4.5 m. Calculate how much m² of sheet metal is needed to cover this roof if 5.5% of the sheet we must add for joints and waste.
• Church roof 2
  The roof has the shape of a rotating cone shell with a base diameter of 6 m and a height of 2.5 m. How many monez (CZK) will cost the roof cover sheet if 1 m² of metal sheet costs 152 CZK and if you need 15% extra for joints, overlays and waste?
• 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?
• Lampshade
  The cone-shaped lampshade has a diameter of 30 cm and a height of 10 cm. How many cm² of material will we need when we 10% is waste?
• Iglu - cone tent
  The cone-shaped tent is 3 m high, the diameter of its base is 3.2 m. a) The tent is made of two layers of material. How many m² of fabric is needed for production (including flooring), if 20% needs to be added to the minimum amount due to cutting waste? b
• Cone roof
  How many m² of roofing is needed to cover a cone-shaped roof with a diameter of 10 m and a height of 4 m? Add an extra 4% to the overlays.
• Roof of the church
  The cone roof of the church has a diameter of 3m and a height of 4m. What is the size of the side edge of the church roof (s) and how much sheet will be needed to cover the church roof?
• Top of the tower
  The top of the tower has the shape of a regular hexagonal pyramid. The base edge has a length of 1.2 m, the pyramid height is 1.6 m. How many square meters of sheet metal is needed to cover the top of the tower if 15% extra sheet metal is needed for joint
• Regular quadrangular pyramid
  How many square meters is needed to cover the tower the shape of regular quadrangular pyramid base edge 10 meters, if the deviation lateral edges from the base plane is 68 °? Calculate coverage waste 10%.
• Storm and roof
  The roof on the building is a cone with a height of 3 meters and a radius equal to half the height of the roof. How many m² of roof need to be repaired if 20% were damaged in a storm?
• 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?
• 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?
• The tent
  The tent shape of a regular quadrilateral pyramid has a base edge length a = 2 m and a height v = 1.8 m. How many m² of cloth we need to make the tent if we have to add 7% of the seams? How many m³ of air will be in the tent?
• 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?
• Rectangular base pyramid
  Calculate an area of the shell of the pyramid with a rectangular base of 2.8 m and 1.4 m and height 2.5 meters.