Question

Find the volume of a pentagonal spherical pyramid whose base has angles of 105°, 115°, 125°, 135°, and 145° on a sphere of radius 10cm.​

Answer 1

Answer:

A= THERE FOR ,THE DESIRED AREA ,

A=[223π/60 (5-2)π](12²)

A= 516π/5= 324.21m² ( 0PTION A.)

Explanation:

THE SPHERICAL POLYGON IS A GENERALIZATION OF THE SPHERICAL TRIANGLE

IF (0-) IS THE SUM OF THE RADIAN ANGLES OF A SPHERICAL POLYGON ON A SPHERE OF RADIUS R, THEN THE AREAS:

A= [(0-)-(n-2)π]R²

TOTAL ANGLES: 223π/60

Answer 2

Concept:

Pyramids are three-dimensional objects having triangular lateral faces and a polygonal foundation. The point where the lateral faces come together is called the pyramid's apex. The base's edges and the apex are connected by the lateral triangular faces.

Spherical pentagonal pyramid:The base of the pyramid is pentagonal in shape (a base with five sides). There are 6 faces, 6 vertices, and 10 edges in the pentagonal pyramid.

If θ is the sum of the radian angles of a spherical polygon on a sphere of radius R, then the area is :

A =[θ-(n-2)π]R²

Given:

A pentagonal spherical pyramid whose base has angles of 105°, 115°, 125°, 135°, and 145° on a sphere of radius 10cm.​

Find:

Find the volume of a pentagonal spherical pyramid

Solution:

If θ is the sum of the radian angles of a spherical polygon on a sphere of radius R, then the area is :

A =[θ-(n-2)π]R²

Sum of radian angles= 21π/36 + 23/36 +25π/36 + 27π/36 + 29π/36

                                   =125π/36

A=[125π/36 -  π(5-2)](10)²

A= 148.37m²

Therefore, the volume of pentagonal spherical pyramid is 148.37 m²

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