Ex 12.1, 3 - Chapter 12 Class 10 Surface Areas and Volumes

Transcript

Ex 12.1, 3 A toy is in the form of a cone of radius 3.5 cm mounted on a hemisphere of same radius. The total height of the toy is 15.5 cm. Find the total surface area of the toy. Total surface area of toy = Curved Surface area of hemisphere + Curved Surface area of cone Curved Surface area of hemisphere Radius of hemisphere = Radius of cone = r = 3.5 cm Curved surface area of hemisphere = 2𝜋𝑟2 = 2 ×22/7× (3.5)2 = 2 ×22/7× (3.5)2 = 2 ×22/7× 3.5 × 3.5 = 2 × 22 × 0.5 × 3.5 = 77 cm2 Curved surface area of cone Curved surface area of cone = 𝝅𝒓𝒍 Radius of cone = r = 3.5 cm Height of cone = Total height of toy – radius of hemisphere = 15.5 – 3.5 = 12 cm Now, we find slant height (l) We know that l2 = h2 + r2 l2 = (12)2 + (3.5)2 l2 = (12)2 + (7/2)^2 l2 = 144 + 49/4 l2 = (144(4) + 49)/4 l2 = (576 + 49)/4 l2 = 𝟔𝟐𝟓/𝟒 l = √(625/4) l = √(25^2/2^2 ) l = 𝟐𝟓/𝟐 l = 12.5 cm Curved surface area of cone = πr𝑙 = 22/7 × 3.5 × 12.5 = 22 × 0.5 × 12.5 = 137.5 cm2 Now, Total surface area of toy = Curved Surface Area of hemisphere + Curved Surface Area of cone = 77 + 137.5 = 214.5 cm2 Hence, total surface area of the toy is 214.5 cm2