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.
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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
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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]
Byju's Answer Standard X Mathematics
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 3A 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.
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
Standard X Mathematics
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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