8.2.1 Solid Geometry III, PT3 Practice


8.2.1 Solid Geometry III, PT3 Practice

Question 1:
The diagram below shows a cone with diameter 14 cm and height 6 cm.
 
Find the volume of the cone, in cm3.
 
Solution:
Volume of a cone = 1 3 π r 2 h = 1 3 × 22 7 × 7 2 × 6 2 = 308 cm 3

 


Question 2:
In the pyramid shown, the base is a rectangle.


If the volume is 20 cm2, find the height of the pyramid, in cm.

Solution:
Volume of a pyramid = 1 3 × base area × h 1 3 × base area × h = 20 1 3 × 5 × 4 × h = 20 20 3 × h = 20 h = 20 × 3 20 h = 3 cm


Question 3:
Diagram below shows a composite solid consisting of a right circular cone, a right circular cylinder and a hemisphere.
 

The volume of the cylinder is 1650 cm3. Calculate the height, in cm, of the cone.
[ Use π= 22 7 ]  

Solution:
Volume of a cylinder = π r 2 h 22 7 × r 2 × 21 = 1650 r 2 = 1650 × 7 22 × 21 = 25 r = 5 c m Thus the height of the cone = 39 5 21 = 13 c m


Question 4:
The cross section of the prism shown is an isosceles triangle.
 
The volume of the prism, in cm3, is

Solution:
Height of the = 10 2 6 2 = 64 = 8 c m Volume of prism = Area of cross section × Length = ( 1 2 × 12 6 × 8 ) × 16 = 768 c m 3



Question 5:
A right circular cone has a volume of 77 cm3 and a circular base of radius 3.5 cm. Calculate its height.

Solution:
V= 1 3 π r 2 h h= 3V π r 2   = 3×77 22 7 ×3.5×3.5   =6 cm


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