A toy is in the shape of a right circular cylinder with a hemisphere on one end and a cone on the other. The radius and height of the cylindrical part are 5 cm and 13 cm respectively. The radii of the hemispherical and conical parts are the same as that of the cylindrical part. Find the surface area of the toy if the total height of the toy is 30 cm.
Answers
Answer:
The Surface area of the toy = 770 cm²
Step-by-step explanation:
Given:
Radius of the hemisphere = Radius of the base of the cylinder = Radius of the base of the cone , r = 5 cm
Height of the hemisphere = radius of hemisphere = 5 cm.
Height of the cylindrical part ,H = 13 cm
Total height of the toy = 30 cm
Let the height of the cone be h cm
Total height of the toy = height of the hemisphere + height of the cylinder + height of the cone
30 = 5 +13 + h
30 = 18 + h
height of cone= 30-18
height of cone, h = 12cm
Slant height of the cone (l) = √r² + h²
l = √ 5² +12²
l = √25 +144 = √169
l = 13 cm
Surface area of the toy = Curved surface area of the hemisphere + curved surface area of the cylinder + curved surface area of the cone.
Surface area of the toy = 2πr² + 2πrh + πrl
= πr ( 2r + 2h + l)
= π× 5 (2×5 + 2× 13 + 13)
= π × 5 ( 10 +26 +13)
= π × 5 (49)
= 22/7 × 5 × 49
= (110 × 7)
= 770 cm²
Hence, the Surface area of the toy = 770 cm²
HOPE THIS ANSWER WILL HELP YOU…
Step-by-step explanation:
Height of the cylindrical part =13cm
Radius of cone , cylinder and hemi sphere=5cm
r=5cm for hemisphere cylinder and cone.
Height of cone h=30−5−13=12
The area of canvas required=Surface area of hemishphere,cylinder and cone parts of tent
A=2πr 2+2πrH+πr( h 2 +r 2 )
A=2π×5×5+2π×5×13+π×5(5 2 +12\2 )
A=770cm 2