there are two wooden square prisms with base edge 8cm and height 12cm.from one of this prism ajesh curved outthe largest square pyramid.but from the otherrajesh curved out the largest cone.find the volume of the solids they curved out.whose product has greater volume
To find the volume of the solid shapes curved out by Ajesh and Rajesh, we need to calculate the volumes of the square pyramid and the cone.
1. Ajesh's Square Pyramid:
The largest square pyramid that can be curved out from the wooden prism will have a base equal to the square base of the prism. The height of the pyramid will be equal to half the height of the prism.
Given:
Base edge of the prism = 8 cm
Height of the prism = 12 cm
The volume of a square pyramid is given by the formula: V = (1/3) * base area * height
Base area of the pyramid = (base edge)^2 = 8^2 = 64 cm^2
Height of the pyramid = (1/2) * Height of the prism = (1/2) * 12 = 6 cm
Using the formula, we can find the volume of Ajesh's square pyramid:
V_square_pyramid = (1/3) * 64 * 6
= 128 cm^3
2. Rajesh's Cone:
The largest cone that can be curved out from the wooden prism will have a base equal to the square base of the prism. The height of the cone will be equal to the height of the prism.
Given:
Base edge of the prism = 8 cm
Height of the prism = 12 cm
The volume of a cone is given by the formula: V = (1/3) * base area * height
Base area of the cone = (base edge)^2 = 8^2 = 64 cm^2
Height of the cone = Height of the prism = 12 cm
Using the formula, we can find the volume of Rajesh's cone:
V_cone = (1/3) * 64 * 12
= 256 cm^3
Comparing the volumes:
V_square_pyramid = 128 cm^3
V_cone = 256 cm^3
So, the volume of the solid curved out by Rajesh (cone) is greater than the volume of the solid curved out by Ajesh (square pyramid).