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=13πr2h=13×227×72×62=308cm3

 


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=13×base area×h13×base area×h=2013×5×4×h=20203×h=20h=20×320h=3cm


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=227]  

Solution:
Volume of a cylinder=πr2h227×r2×21=1650r2=1650×722×21=25r=5cmThus the height of the cone=39521=13cm


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=10262=64=8cmVolume of prism=Area of cross section×Length=(12×126×8)×16=768cm3



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=13πr2hh=3Vπr2  =3×77227×3.5×3.5  =6 cm