Example 1 - Chapter 12 Class 10 Surface Areas and Volumes

Transcript

Example 1 Rasheed got a playing top (lattu) as his birthday present, which surprisingly had no colour on it. He wanted to colour it with his crayons. The top is shaped like a cone surmounted by a hemisphere(see figure). The entire top is 5 cm in height and the diameter of the top is 3.5 cm. Find the area he has to colour. (Take = 22/7) Surface area to colour = Surface Area of hemisphere + Curved Surface Area of cone Surface Area of hemisphere Diameter of hemisphere = 3.5 cm So, radius = r = 3.5/2 Surface Area of hemisphere = 2 2 = 2 22/7 (3.5/2)^2 = 2 22/7 3.5/2 3.5/2 = 11 0.5 3.5 = 19.25 cm2 Curved Surface area of cone Curved Surface area of cone = Here, radius = r = 3.5/2 = 1.75 cm Height of cone = height of top radius of hemisphere = 5 1.75 = 3.25 cm We find first We know that l2 = h2 + r2 l2 = (3.25)2 + (1.75)2 l2 =10.56 + 3.0625 l2 = 13.6225 l = ("13.6225" ) l = 3.69 cm Curved Surface area of cone = = 22/7 3.5/2 3.6 = 11 0.5 3.6 = 19.8 cm2 Hence, Surface area of the top = Surface area of hemisphere + Curved Surface area of cone = 19.25 + 19.8 = 39.05 Hence, area of the top = 39.05 cm2