6.5.2 Volume of Three Dimensional Shapes, PT3 Practice


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



Question 6:
Puan Rafidah wants to prepare a right circular cone shaped container in order to fill it with candies for her family Hari Raya Celebration. Diagram below shows the net of a right circular cone.

The circumference of the lid is 44 cm and its height is 24 cm.
Calculate the volume, in cm3 , of the container.
[ π= 22 7 ]

Solution:
2πr=44 2× 22 7 ×r=44  r= 44 2 × 7 22  r=7 cm Volume of cone= 1 3 π r 2 h  = 1 3 × 22 7 × 7 2 ×24  =1232  cm 3


Question 7:
A barrel contains 36 l of mineral water. ⅔ of the mineral water is mixed with 6 bottles of syrup, with a volume of 1.5 l each. The drink will be poured into a number of bottles with the same volume of 300 ml.
How many number of bottles needed?

Solution:
Volume of mineral water = 2 3 ×36 l =24 l Volume of syrup =6×1.5 l=9 l Total volume=24+9 =33 l=33000 ml Number of bottles needed = 33000 300 =110

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