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A Cylindrical Vessel with Internal Diameter 10 Cm and Height 10.5 Cm is Full of Water. a Solid Cone of Base Diameter 7 Cm and Height 6 Cm is Completely Immersed in Water. Find the Value of Water (I) Displaced Out of the Cylinder (Ii) Left in the Cylinder. (Take π 22/7) - Mathematics

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Question

A cylindrical vessel with internal diameter 10 cm and height 10.5 cm is full of water. A solid cone of base diameter 7 cm and height 6 cm is completely immersed in water. Find the value of water (i) displaced out of the cylinder (ii) left in the cylinder. (Take π 22/7)

Solution

We have a cylindrical vessel in which a cone is inserted. We have,

Radius of the cylinder(r1) = 5 cm

Radius of cone(r2) = 3.5 cm

Height of cylinder(h) = 10.5 cm

Height of cone(l) = 6 cm

(i) We have to find the volume of water displaced from the cylinder when cone is inserted.

So,

Volume of water displace = volume of cone

So volume of water displaced,

=1/3pir_2^2l

=1/3(22/7)(12.25)(6) cm^3

= 77 cm3

(ii) We have to find the volume of water remaining in the cylinder.

Volume of water left = Volume of cylinder - Volume of cone

So volume of the water left in the cylinder,

=[(22/7(25)(10.5))-(77)] cm^3

=(825-77)cm3

= 748 cm3

Is there an error in this question or solution?

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RD Sharma Solution for Class 10 Maths (2018 (Latest))
Chapter 14: Surface Areas and Volumes
Ex. 14.2 | Q: 24 | Page no. 62
Solution A Cylindrical Vessel with Internal Diameter 10 Cm and Height 10.5 Cm is Full of Water. a Solid Cone of Base Diameter 7 Cm and Height 6 Cm is Completely Immersed in Water. Find the Value of Water (I) Displaced Out of the Cylinder (Ii) Left in the Cylinder. (Take π 22/7) Concept: Volume of a Combination of Solids.
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