A drinking glass is in the shape of a frustum of a cone of height 14 cm. The diameters of its two circular ends are 4 cm and 2 cm. Find the capacity of the glass
Solution:
A figure is drawn to visualize the shape.
As mentioned that the glass is in the shape of a frustum of a cone
Therefore, the capacity of the glass = Volume of the frustum of the cone.
Let us find the capacity of the glass by using formulae
Volume of a frustum of a cone = 1/3 πh(r₁2 + r₂2 + r₁r₂), where r₁, r₂, and h are the radii and height of the frustum of the cone respectively.
Height of glass, h = 14 m
Radius of the larger base, r₁ = 4 cm / 2 = 2 cm
Radius of the smaller base, r₂ = 2 cm / 2 = 1 cm
The capacity of the glass = Volume of frustum of a cone = 1/3 πh(r₁2 + r₂2 + r₁r₂)
= 1/3 × 22/7 × 14 cm × (2 cm)2 + (1 cm)2 + 2 cm × 1 cm
= 44/3 cm × (4 cm2 + 1 cm2 + 2 cm2)
= 44/3 cm × 7cm2
= 308/3 cm2
= 102 ⅔ cm2
Therefore, the capacity of the glass is 102 ⅔ cm3.
☛ Check: NCERT Solutions Class 10 Maths Chapter 13
Video Solution:
A drinking glass is in the shape of a frustum of a cone of height 14 cm. The diameters of its two circular ends are 4 cm and 2 cm. Find the capacity of the glass.
NCERT Solutions for Class 10 Maths Chapter 13 Exercise 13.4 Question 1
Summary:
The capacity of the frustum of a cone shaped drinking glass of height 14 cm having diameters of its circular ends as 4 cm and 2 cm is 102 ⅔ cm3
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