a solid toy in the form of a hemisphere surmounted by a right circular cone of same radius the height of the cone is 10 cm and the radius of the base is 7 cm determine the volume of the toy also find the area of the colour sheet required to cover the toy use Pi is equal to 22 by 7 square root 149 is equal to 12.2
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The volume of the toy is 1232 cm³ and the area of the colour sheet is 576.4 cm²
Given that, the height of the cone is (h) = 10cm
The radius of the base is (r) = 7cm
We know that the volume of the cone of height h and radius r is given by
V = (1/3)Пr²h
Putting the respective values, we get,
V = (1/3)П(7)²(10) cm³
= 490П/3 cm³
The volume of the hemisphere of radius 7cm is given by
V' = (2/3)Пr³
= (2/3)П(7)³
= 686П/3 cm³
Total volume = V + V'
= (490П/3 + 686П/3) cm³
= 392П cm³
= (392*22/7) cm³
= 1232 cm³
Let the slant height be l cm
l = √(r²+h²)
= √(7²+10²)
= 12.2cm
So, curved surface area of the cone Пrl
Putting the respective values, we get
CSA = П(7)(12.2) cm²
= 85.4П cm²
CSA of hemisphere = 2Пr² cm²
= 2П(7)² cm²
= 98П cm²
Total area = (85.4+98)П cm²
= 183.4П cm²
= (183.4*22/7) cm²
= 576.4 cm²