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 13
Video 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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