
Geometry  solid figures
solved problems 



Solid figures, solved problems examples 





Example:
A point source of light is 4
m distant from the center of a sphere of radius
2
m^{}. What surface area of the sphere
is brightened? 
Solution: Given
R
= 2 m and
SA
= 4 m. S
_{cap}
= ? 

Example:
Edges of a cuboid (rectangular prism) are in ratio 1
: 2 : 5 and length of its diagonal
5Ö6. Surface of the cuboid is? 
Solution: Given
a
: b
: c
= 1
: 2
: 5 and D_{
}= 5Ö6
. S
_{rectangular
prism} = ? 

Example:
The base of a pyramid is regular pentagon and the lateral faces are equilateral triangles. The
basetoface dihedral
angle is? 
Solution: Given a
regular
pentagonal pyramid.
a
= ? 

Example:
On a horizontal surface placed are four spheres of the same radius
R
such that they touch each other and their
centers form square. Onto these four spheres placed is the fifth sphere of the same radius
which touches all the
four. The distance of the center of the fifth sphere from the horizontal surface is? 
Solution: Given
R.
x
= ? 

Example:
An isosceles trapezoid rotates around line which passes through midpoints of its bases. If longer
basis is 10
cm,
shorter 6
cm
and leg 4
cm, find volume and surface of generated solid of revolution. 
Solution: Given
a
= 10 cm, c
= 6 cm
and b
= 4 cm. V_{s.r.}
= ?
and S_{s.r.}
= ? 



Example:
A right triangle with legs a
and b
and the hypotenuse c
first rotates around the leg a
and then around the leg b.
Find the ratio of volumes of generated solids of revolution. 
Solution: Given a
and b.
V_{s.r.}_{
 }_{a}
: V_{s.r.
 }_{b}
= ? 

Example:
Sides of a triangle are 34,
20
and 18
cm^{} long. Find the volume of a solid generated by rotation
of
the triangle
around a line passing through the vertex opposite of triangles' longest side and which is parallel to
it. 
Solution: Given
a
= 34 cm, b
= 20 cm
and c
= 18 cm. V_{s.r.}
= ? 


Example:
A triangle with sides 5,
4
and 3
cm, rotates around the longest side, find the volume of the solid of revolution. 
Solution: Given
a
= 5, b
= 4 and c
= 3. V_{s.r.}
= ? 










Geometry
and use of trigonometry contents  B 



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