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.
Answers

Type your question...

10th
Maths
Surface Areas and Volumes
Surface Area and Volumes
A toy is in the form of a c...
MATHS
Asked on December 20, 2019 bySaptarshi Swaraj
A toy is in the form of a cone mounted on a hemisphere of radius 3.5 cm . The total height of the toy is 15.5cm . Find the total surface area and volume of the toy .
MEDIUM
Share
Save
ANSWER
Given: toy in form of a cone mounted on a hemisphere
radius of hemisphere =3.5 cm
Total height of toy =15.5 cm
To find: Total surface area TSA = ? Volume, V = ?
Solution :
h=12 cm
r=3.5 cm
Assuming that the cone is completed mounted on hemisphere
TSA of toy = CSA of cone + CSA of hemisphere
=πrl+2πr2 [r→ radius of both cone and hemisphere as it is here]
=πr[l+2r]
=722×1035[(12)2+(3.5)2+2×1035]
=11[144+12.25+7]=11[156.25+7]
=11(12.5+7)
=11×19.5
=214.5cm2
Volume of toy = 31πr2h+32
Answer:
We have,
Radius of cone = Radius of hemisphere = 3.5 cm.
Height of the toy = 15.5 cm
To calculate the CSA of cone we have to find first the Slant Height of the cone :]
Slant Height = h² + r²
Slant Height = (15.5)² + (3.5)²
Slant Height = 12.25 + 144
Slant Height = 156.25 cm²
Slant Height = 12.5 cm
Now, we will calculate the TSA of the toy :
➳ TSA of toy = CSA of hemisphere + CSA of cone
➳ TSA of toy = 2πr² + πrl
➳ TSA of toy = 2π(3.5)² + π(3.5)(12.5)
➳ TSA of toy = 24.5π + 43.75π
➳ TSA of toy = 68.25π
➳ TSA of toy = 68.25 * 22/7
➳ TSA of toy = 214.5 cm²