solid geometry

Question

A solid metallic sphere with a radius of 7 cm is cut into 4 similar parts of equal volume. what is the total surface area of each part ?

 

(a)410

(b)325

(c)300

(d)308

Answer 1

Imagine taking the sphere and cutting it in half.  Each half will have a curved portion with half of the original surface area plus the area of a circle with the given radius (7cm)

 

Now take one of the half spheres and cut it again ... we now have a wedge with the curved portion having 1/4 of the original sphere's surface area and two flat semi-circles of the given radius.  The two flat semicircles will equate to the area of one circle of the original radius. 

 

That means each wedge will have a surface area equal to 1/4 of the original surface area plus the area of a circle of the original radius.

 

Surface Area of a sphere is found by A = 4∏r²  so (1/4)A = ∏r² = 49∏

This is the surface area of the curved part of each wedge

 

The circle area is found by A = ∏r² = 49∏

 

Thus the total surface area of each wedge is 49∏ + 49∏ = 98∏ ≅ 307.87 ≅ 308 cm²