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 answer:

S =  548.3641 m²

Step-by-step explanation:

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

Try another example

Related math problems and questions:

• 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?
• 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 add one-third to the overlap.
• 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.
• 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
• 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?
• 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?
• 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.
• 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?
• The roof of the church
  The cone roof of the church has a diameter of 3 m and a height of 4 m. What is the size of the side edge of the church roof (s=?) and many sheets sheet will be needed to cover the church roof?
• 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?
• 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
• Tower
  How many m² of the copper plate should be replaced on the roof of the tower conical shape with diameter 24 m, and the angle at the axial section's vertex is 144°?
• The roof
  The roof of the tower has the shape of a regular quadrangular pyramid, the base edge of which is 11 m long and the side wall of the animal with the base an angle of 57°. Calculate how much roofing we need to cover the entire roof, if we count on 15% waste
• Cone - from volume surface area
  The volume of the rotating cone is 1,018.87 dm³, and its height is 120 cm. What is the surface area of the cone?
• Cone and the ratio
  The rotational cone has a height 23 cm, and the ratio of the base surface to lateral surface is 7: 9. Calculate the surface of the base and the lateral surface.
• The conical
  The conical candle has a base diameter of 20 cm and a side of 30 cm. How much dm ^ 3 of wax was needed to make it?
• Metal washers
  Metal washers with a diameter of 80 mm are cut from a strip of steel sheet with a width of 10 cm and a length of 2 m. Calculate the percentage of material waste if no material is lost when two adjacent circles meet.