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.
Given that the radius of the cone and the hemisphere (r) = 3.5 cm or 7/2 cm
The total height of the toy is given as 15.5 cm.
So, the height of the cone (h) = 15.5 - 3.5
= 12 cm
Slant height of the cone(l) = \(\sqrt{h^2 + r^2}\)
l = \(\sqrt{(12)^2 + (3.5)^2}\)
l = \(\sqrt{(12)^2 + (\frac{7}{2})^2}\)
l = \(\sqrt{144 + (\frac{49}{4})}\)
l = \(\sqrt{\frac{576+49}{4}}\)
= \(\sqrt{\frac{625}{4}}\)
l = \(\frac{25}{2}\)
∴ The curved surface area of cone = πrl
= 22/7)×(7/2)×(25/2) = 275/2 cm2
Also, the curved surface area of the hemisphere = 2πr2
= 2 × (22/7) × (7/2)2
= 77 cm2
Total surface area of the toy = CSA of cone + CSA of hemisphere
= (275/2)+77 cm2
= (275+154)/2 cm2
= 429/2 cm2
= 214.5 cm2
So, the total surface area (TSA) of the toy is 214.5 cm2