A toy consists of a cylinder with a hemisphere at one end and cone at other end with same radius which is 7 cm.
The height of conical part is 12cm while that of cylindrical part is 40cm. Find the total surface area and volume of
the toy
Answers
Answer:
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 5cm and 13cm 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 30cm.
ANSWER
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
Step-by-step explanation:
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Given:
A toy consists of a cylinder with a hemisphere at one end and cone at other end with same radius which is 7 cm. The height of conical part is 12cm while that of cylindrical part is 40cm.
To find:
Find the total surface area and volume of the toy.
Solution:
From given, we have the data as follows.
A toy consists of a cylinder with a hemisphere at one end and cone at other end with same radius which is 7 cm. The height of conical part is 12cm while that of cylindrical part is 40cm.
Consider the attached figure while going through the following steps.
The surface area of the toy = surface area of the hemisphere + surface area of the cylinder + surface area of the cone.
The surface area of the toy = 3πr² + 2πr(r + h) + 2πr (r + l)
= 3πr² + 2πr(r + h) + 2πr (r + √(r² + h²)
= 3π (7)² + 2π (7)(7 + 40) + 2π (7) (7 + √(7² + 40²)
= 461.8 + 2067.16 + 2093.9
= 4622.86 cm²
The volume of the toy = volume of the hemisphere + volume of the cylinder + volume of the cone.
The volume of the toy = 2/3 πr³ + πr²h + 1/3 πr²h
= 2/3 π (7)³ + π (7)² (40) + 1/3 π (7)² (40)
= 718.3 + 6157.52 + 2052.5
= 8928.32 cm³
Therefore, the surface area and the volume of the toy is, 4622.86 cm² and 8928.32 cm³ respectively.
