Question

1. A toy is in the form of a cone of redius
3.5cm mounted on a hemisphere of same
redius. the total hight of toy is 15.5 cm.
find the total surface are of the toy?
1.214.5cm2
2. 154cm2​

Answer 1

Given :

• A toy is in the form of a cone of radius
• 3.5 cm mounted on a hemisphere of same
• radius.
• The total hight of toy is 15.5 cm.

To Find :

• We need to find the Total surface area of the toy.

Solution :

As in the question it is stated that , A toy is in the form of a cone of radius 3.5cm mounted on a hemisphere of same radius. So, radius of hemisphere is equal to radius of cone :

• Radius of hemisphere = Radius of cone = 3.5 cm

To find the total surface area of the toy first we need to find the Curved surface area of the hemisphere after finding the CSA of hemisphere we will find the CSA of cone but we are not provided the Slant Height of cone so before finding the CSA of cone we will find the Slant of the cone after finding the Slant Height we will calculate the CSA of cone and at last we will find the Total surface area of the toy by the given below formula :

• TSA of toy = CSA of hemisphere + CSA of cone

Now,let's do it :

◖C S A O F H E M I S P H E R E :

→ CSA of hemisphere = 2πr²

→ CSA of hemisphere = 2 × 22/7 × (3.5)²

→ CSA of hemisphere = 2 × 22/7 × 12.25

→ CSA of hemisphere = 24.5 × 22/7

→ CSA of hemisphere = 3.5 × 22

→ CSA of hemisphere = 77 cm²

◖H E I G H T O F C O N E :

↛Height of the cone = Total height of toy - Radius

↛Height of the cone = 15.5 - 3.5

↛Height of the cone = 12 cm

◖S L A N T H E I G H T O F C O N E :

⇏(Slant Height)² = (Height)² + (Radius)²

⇏(Slant Height)² = (12)² + (3.5)²

⇏(Slant Height)² = 144 + 12.25

⇏(Slant Height)² = 156.25

⇏(Slant Height) = √156.25

⇏(Slant Height) = 12.5 cm

◖C S A O F C O N E :

⇢CSA of cone = πrl

⇢CSA of cone = 22/7 × 3.5 × 12.5

⇢CSA of cone = 22/7 × 43.75

⇢CSA of cone = 22 × 6.25

⇢CSA of cone = 137.5 cm²

◖T S A O F T H E T O Y :

⇻TSA of toy = CSA of hemisphere + CSA of cone

⇻TSA of toy = 2πr² + πrl

⇻TSA of toy = 77 + 137.5

⇻TSA of toy = 214.5 cm²

∴ Total surface area of the toy is 214.5 cm².