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# a toy is in the form of a cone of radius 3.5 cm mounted on a hemisphere of same radius on its circular face. the total height of the toy is 15.5 cm. find the total surface area of the toy.

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## A toy in the form of 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 toy.

Click here👆to get an answer to your question ✍️ A toy in the form of 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 toy. Question

## A toy in the form of 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 toy.

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Updated on : 2022-09-05

Solution Verified by Toppr

Total surface area of toy =  Curved surface area of cone +  surface area of hemisphere

Curved  surface area of cone = πrl

Where r=3.5cm, Height =15.5−3.5=12cm

And hence, l=12.5cm       (by using formula l

2 =h 2 +b 2 )

Therefore C.S.A. of cone =π×3.5×12.5

=137.5cm 2

Surface area of hemisphere =2πr

2 =2×π×(3.5) 2 =77cm 2

Hence T.S.A of toy =77+137.5=214.5cm

2

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## A 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. [4 MARKS]

A 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. [4 MARKS] Surface Area of a Hemisphere

A toy is in t... Question

A 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. [4 MARKS]

Open in App Solution Concept: 1 Mark

Application: 3 Marks

Radius of Cone = r = 3.5 cm

Total Height of toy = 15.5 cm

Radius of Hemisphere = radius of cone = r = 3.5 cm Height of cone = h ⇒ A O = h

h = Total height of toy - radius of hemisphere = 15.5 - 3.5 = 12 cm

In Δ A O B

, AO = h = Height of cone,

we can apply Pythagoras Theorem to find slant height of the cone.

Slant height of cone

= A B = l = √ r 2 + h 2 = √ ( 3.5 ) 2 + ( 12 ) 2 = √ 12.25 + 144 = √ 156.25 = 12.5 c m

Total surface area of toy

=

Surface area of Cone + Surface area of Hemisphere

= π . r . l + 2. π . r 2 = ( 22 7 × 3.5 × 12.5 ) + 2 × 22 7 × 3.5 × 3.5 = 137.5 + 77 = 214.5 c m 2 Suggest Corrections 177 SIMILAR QUESTIONS

Q. Question 3

A 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. Q. A toy is in the from of a cone of radius

3.5 c m

mounted on a hemisphere of same radius. The total height of the toy is

15.5 c m

. Find the total surface of the toy (in

c m 2 ).

Q.

A toy is in the form of a cone mounted on a hemisphere of radius 3.5 cm. If the total height of the toy is 15.5 cm, then its total surface area is

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Surface Area of a Hemisphere

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स्रोत : byjus.com

## A 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.

A 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. The total surface area of the conical toy of radius 3.5 cm mounted on a hemisphere of the same radius is 214.5 cm^2. ## A 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

Solution:

We can create the figure of the toy as per the given information From the figure, it’s clear that the total surface area of the toy includes the curved surface area (CSA) of the cone and hemisphere.

Total surface area of the toy = CSA of the hemisphere + CSA of the cone

We will find the total area of the toy by using formulae;

CSA of the hemisphere = 2πr2, where 'r' is the radius of the hemisphere

CSA of the cone = πrl, where 'r' and 'l' are the radius and slant height of the cone respectively.

Radius of the hemisphere, r = 3.5 cm

Height of the hemisphere = radius of the hemisphere, r = 3.5 cm

Radius of the cone, r = 3.5 cm

Height of the cone = Total height of the toy - height of the hemisphere

h = 15.5 cm - 3.5 cm = 12 cm

Slant height of the cone, l = √(r2 + h2)

l = √[(3.5 cm)2 + (12 cm)2]

l = √[12.25 cm2 + 144 cm2]

l = √ 56.25 cm2 l = 12.5 cm

Total surface area of the toy = CSA of the hemisphere + CSA of the cone

= 2πr2 + πrl = πr (2r + l)

= 22/7 × 3.5 cm × (2 × 3.5 cm + 12.5 cm)

= 22/7 × 3.5 cm × (7 cm + 12.5 cm)

= 11 cm × 19.5 cm = 214.5 cm2

Thus, the total surface area of the toy is 214.5 cm2.

☛ Check: NCERT Solutions for Class 10 Maths Chapter 13Video Solution:

## A 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

NCERT Solutions Class 10 Maths Chapter 13 Exercise 13.1 Question 3

Summary:

The total surface area of the conical toy of radius 3.5 cm mounted on a hemisphere of the same radius if the total height of the toy is 15.5 cm is 214.5 cm2.

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Mohammed 4 day ago

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