From a solid cylinder whose height is 8 𝑐𝑚 and radius 6 𝑐𝑚, a conical cavity of same height and same base radius is hollowed out. Find the total surface area of the remaining solid. (Take π = 3. 14)

Question

From a solid cylinder whose height is 8  and radius 6 , a conical cavity of same height and same base radius is hollowed out. Find the total surface area of the remaining solid. (Take π = 3. 14)

Infinity Learn · Accepted Answer

We have been given the height (8 𝑐𝑚) and radius (6 𝑐𝑚) of cylinder, whose conical cavity of same height and same base radius is hollowed out. We need to find the total surface area of the remaining solid.

From the given information, we can say that

𝐻𝑒𝑖𝑔ℎ𝑡 𝑎𝑛𝑑 𝑟𝑎𝑑𝑖𝑢𝑠 𝑜𝑓 𝑐𝑦𝑙𝑖𝑛𝑑𝑒𝑟 = ℎ𝑒𝑖𝑔ℎ𝑡 𝑎𝑛𝑑 𝑟𝑎𝑑𝑖𝑢𝑠 𝑜𝑓 𝑐𝑜𝑛𝑒

Slant height (𝑙) of a cone can be expressed as $𝑙 = \sqrt{r^{2} + h^{2}}$ where 𝑟 is the radius of the cone and ℎ is the its height.

$l = \sqrt{6^{2} + 8^{2}}$

𝑙 = 10 cm

Now, 𝑆𝑢𝑟𝑓𝑎𝑐𝑒 𝑎𝑟𝑒𝑎 = 𝑆𝑢𝑟𝑓𝑎𝑐𝑒 𝑎𝑟𝑒𝑎 𝑜𝑓 (𝑐𝑢𝑟𝑣𝑒𝑑 𝑐𝑦𝑙𝑖𝑛𝑑𝑒𝑟 𝑠𝑢𝑟𝑓𝑎𝑐𝑒 + 𝑐𝑜𝑛𝑒 + 𝑡𝑜𝑝 𝑜𝑓 𝑐𝑦𝑙𝑖𝑛𝑑𝑒𝑟)

We know that, Surface area of cylinder = 2π𝑟ℎ

Surface area of cone = π𝑟𝑙

Area of top of cylinder= π𝑟 2

= 2π𝑟ℎ + π𝑟𝑙 + π𝑟 2

= π𝑟(2ℎ + 𝑙 + 𝑟)

= 3. 14 × 6 × (2 × 8 + 10 + 6)