A solid is in the shape of a cone standing on a hemisphere with both their radii being equal to 1 cm and the height of the cone is equal to its radius. Find the volume of the solid in terms of π
Solution:
The visualization of the solid figure is drawn below.
The volume of a solid is the space occupied inside it or the capacity that an object holds.
As the solid is made up of a conical part and a hemispherical part,
Volume of the solid = volume of the conical part + volume of the hemispherical part
Let us find the volume of the solid by using formulae;
Volume of the hemisphere = 2/3 πr3 where r is the radius of the hemisphere
Volume of the cone = 1/3 πr2h where r and h are the radius and height of the cone respectively.
Radius of hemispherical part = Radius of conical part = r = 1 cm
Height of conical part = h = r = 1 cm
Volume of the solid = volume of the conical part + volume of the hemispherical part
= 1/3 πr2h + 2/3 πr3
= 1/3 πr3 + 2/3 πr3 [Since, h = r]
= πr3
= π (1cm)3
= π cm3
Thus, the volume of the solid is π cm3.
☛ Check: NCERT Solutions Class 10 Maths Chapter 13
Video Solution:
A solid is in the shape of a cone standing on a hemisphere with both their radii being equal to 1 cm and the height of the cone is equal to its radius. Find the volume of the solid in terms of π
NCERT Solutions Class 10 Maths Chapter 13 Exercise 13.2 Question 1
Summary:
The volume of a solid of a cone standing on a hemisphere with both their radii being equal to 1 cm and the height of the cone being equal to its radius is π cm3.
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