In figure 7.11, a toy made from a hemisphere, a cylinder and a cone is shown. Find the total area of the toy.
Answers
For the Cone,
Radius = 3 cm.
Height = 4 cm.
∴ Slant height (l) = √(16+ 9) = √25 = 5
Using the Formula,
Curved surface area of the cone = πrl
= 22/7 × 3 × 5
= 47.14 cm².
For the cylinder,
Radius = 3 cm.
Height = 40 cm.
Curved surface area of the cylinder = 2πrh
= 2 × 22/7 × 3 × 40
= 754.29 cm²
For the Hemisphere,
Radius = 3 cm.
Curved surface area of the hemisphere = 2πr²
= 2 × 22/7 × 3 × 3
= 56.57 cm²
Hence, the total surface area of the Toy = Curved surface area of the cone + Curved surface area of the cylinder + Curved surface area of the hemisphere.
= 47.14 cm² + 754.29 cm² + 56.57 cm²
= 858 cm²
Hope it helps. :-)
Hi ,
1 ) Dimensions of the hemisphere ;
Radius ( r ) = 3 cm
Surface area of the Hemisphere = A1 = 2πr²
2 ) Dimensions of the cylindrical shape ;
Radius ( r ) = 3 cm
Height ( H ) = 40 cm
Surface area of the cylinder ( A2 ) = 2πrH
3 ) Dimensions of the cone shape ;
radius = r = 3 cm
height ( h1 ) = 4 cm
let slant height = l
l = √ r² + h²
l = √ 3² + 4²
l = 5 cm
Surface area of the cone ( A3 ) = πrl
4 ) Total surface area of the toy = A1 + A2 + A3
= 2πr² + 2πrH + πrl
= πr( 2r + 2H + l )
= 22/7 × 3 ( 2×3 + 2×40 + 5 )
= 22/7 × 3 × 91
= 858 cm²
I hope this helps you.
: )