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A cone is inscribed in a cylinder. A square pyramid is inscribed in a rectangular prism. The cone and the pyramid have the same volume. Part of the volume of the cylinder, V1, is not taken up by the cone. Part of the volume of the rectangular prism, V2, is not taken up by the square pyramid. What is the relationship of these two volumes, V1 and V2?

Respuesta :

v1 is equal to v2. that is your answer

Solution:

Statements regarding cone and Cylinder

Cone is inscribed in the cylinder. Part of the volume of the cylinder, V1, is not taken up by the cone.

V 1= Volume of Cylinder -  Volume of Cone------------(1)

Statements regarding square pyramid and rectangular prism.

Square pyramid is inscribed in a rectangular prism.Part of the volume of the rectangular prism, V2, is not taken up by the square pyramid.

V 2 =  Volume of  rectangular prism - Volume of Square pyramid----------(2)

Volume of Cone=  Volume of Square pyramid-------(3)

Volume of Cylinder= Base Area × Height=πr²h

Volume of  rectangular prism= Base Area × Height=L×B×H→As base is a rectangle.

There are three Possibilities

1. V 1 > V 2→→[If Volume of Cylinder> Volume of  rectangular prism i.e if their base area of cylinder is greater than base area of rectangular prism.]

2. V 2 > V 1 →→[If Volume of Cylinder< Volume of  rectangular prism i.e if their base area of cylinder is smaller than base area of rectangular prism.]

3. V 1 = V 2→→[If Volume of Cylinder= Volume of  rectangular prism i.e if their base area of cylinder is equal to the base area of rectangular prism]



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