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.

Correct answer:

S =  197.5848 m²

Step-by-step explanation:

$$\begin{gathered} D=10\text{ m } \\ h=8\text{ m } \\ r=D\mathrm{/}2=10\mathrm{/}2=5\text{ m } \\ s=\sqrt{h^2+r^2}=\sqrt{8^2+5^2}=\sqrt{89}\text{ m}\doteq 9.434\text{ m } \\ {S}_1=\pi \cdot r\cdot s=3.1416\cdot 5\cdot 9.434\doteq 148.1886{\text{m}}^2 \\ S=(1+{\displaystyle \frac{1}{3}})\cdot S_1=(1+{\displaystyle \frac{1}{3}})\cdot 148.1886=197.5848{\text{m}}^2 \end{gathered}$$

Try another example

Related math problems and questions:

• 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.
• 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?
• 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.
• 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?
• 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?
• Cone container
  Rotary cone-shaped container has a volume 1000 cubic cm and a height 12 cm. Calculate how much metal we need for making this package.
• Cap
  Jesters hat is shaped by a rotating cone. Calculate how much paper is needed to the cap 54 cm high when the head circumference is 47 cm.
• Pyramid roof
  2/4 of the area of ​​the roof-shaped regular tetrahedral pyramid with base edge 10 m and height of 4 m is already covered with roofing. How many square meters still need to be covered?
• 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
• 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?
• 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?
• Surface of the cone
  Calculate the surface of the cone if its height is 8 cm and the volume is 301.44 cm³.
• Castle model
  The castle model has a cone-shaped roof. The cone side is 45 cm long and the base radius is 27 cm. a) What is the roof volume? b) How many dm² of wallpaper is used to glue the roof, ie the cone shell? c) What is the weight of the roof if it is made of woo
• The Indian tent
  The Indian tent is cone-shaped. Its height is 3.5 m. The diameter of the base is 2.5 m. How much canvas is needed to make a tire?
• Cone side
  Calculate the volume and area of the cone whose height is 10 cm and the axial section of the cone has an angle of 30 degrees between height and the cone side.
• The rotating
  The rotating cone has a height of 0.9 m and the diameter of the base is 7.2 dm. Calculate the surface of the cone. (Hint: use Pythagorean theorem for a side of cone)
• 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?