A metallic spherical shell of internal and external diameters 4 cm and 8 cm, respectively is melted and recast into the form a cone of base diameter 8cm. The height of the cone is
a. 12cm
b. 14cm
c. 15cm
d. 18cm
Solution:
It is given that
Internal diameter d1 = 4 cm
Internal radius of spherical shell r1 = 4/2 = 2 cm
External diameter d2 = 8 cm
External radius of spherical shell r2 = 8/2 = 4 cm
Base diameter of cone = 8 cm
Base radius of cone r = 4 cm
Consider h as the height of cone
We know that
Volume of spherical shell= 4/3 π (r2³ - r1³)
where r1 and r2 are internal and external radii.
Volume of spherical shell = 4/3 π (4³ - 2³)
= 4/3 π (56)
= (224/3) π
We know that
Volume of cone = (1/3) πr²h,
Where r is the base radius
h is the height of cone
Volume of cone = (1/3) π4²h = 16πh/3
Here
Volume of spherical shell = Volume of cone recast by melting
224π /3 = 16πh /3
By further simplification
16h = 224
Dividing both sides by 16
h = 14 cm
Therefore, the height of the cone is 14 cm.
✦ Try This: A metallic spherical shell of internal and external diameters 2 cm and 4 cm, respectively is melted and recast into the form a cone of base diameter 6cm. The height of the cone is
☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 13
NCERT Exemplar Class 10 Maths Exercise 12.1 Problem 9
A metallic spherical shell of internal and external diameters 4 cm and 8 cm, respectively is melted and recast into the form a cone of base diameter 8cm. The height of the cone is a. 12cm, b. 14cm, c. 15cm, d. 18cm
Summary:
A metallic spherical shell of internal and external diameters 4 cm and 8 cm, respectively is melted and recast into the form of a cone of base diameter 8cm. The height of the cone is 14 cm
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