Question

A tent is in the shape of a cylinder surmounted by a cone. The slant height of the cone is 2.1 m, and the height of the cylinder is 1.4 m. If the diameter of the cylinder is 2 m, find the total amount of cloth required to construct the tent.

Answer 1

𝑪𝒐𝒏𝒆: 𝑆𝑙𝑎𝑛𝑡 ℎ𝑒𝑖𝑔ℎ𝑡 (𝑙) = 2.1 𝑚

𝐷𝑖𝑎𝑚𝑒𝑡𝑒𝑟 = 2 𝑚

∴𝑅𝑎𝑑𝑖𝑢𝑠 = 1 𝑚

𝑪𝒚𝒍𝒊𝒏𝒅𝒆𝒓: 𝐻𝑒𝑖𝑔ℎ𝑡 (𝐻) = 1.4 𝑚

𝐷𝑖𝑎𝑚𝑒𝑡𝑒𝑟 = 2 𝑚

∴𝑅𝑎𝑑𝑖𝑢𝑠 (𝑟) = 1 𝑚

𝑇𝑜𝑡𝑎𝑙 𝑎𝑚𝑜𝑢𝑛𝑡 𝑜𝑓 𝑐𝑙𝑜𝑡ℎ = 𝐶𝑢𝑟𝑣𝑒𝑑 𝑠𝑢𝑟𝑓𝑎𝑐𝑒 𝑎𝑟𝑒𝑎 𝑜𝑓 𝑐𝑦𝑙𝑖𝑛𝑑𝑒𝑟 + C𝑢𝑟𝑣𝑒𝑑 𝑠𝑢𝑟𝑓𝑎𝑐𝑒 𝑎𝑟𝑒𝑎 𝑜𝑓 𝑐𝑜𝑛𝑒

=(2𝜋𝑟𝐻) + (𝜋𝑟𝑙)

=𝜋𝑟(2𝐻+𝑙)

=(22/7) × 1 × ((2 × 1.4) + 2.1)

=15.4 $m^2$