GCSE Mathematics Question Analysis Topic: Mathematics - Short Questions
Exam Questions:
1) If the total surface area of a solid hemisphere is 462 cm2, find its volume.
2) Water in a canal, 6 m wide and 1.5 m deep, is flowing at a speed of 4 km/h. How much area will it irrigate in 10 minutes, if 8 cm of standing water is needed for irrigation?
Answers:
For GCSE Mathematics, you should know:
1) The total surface of the hemisphere is 462 cm2, from 2πr2.
> 462 = 3πr2
> r = 7 cm.
The volume of the hemisphere is 2/3 x πr3.
so V = 2 / 3 x 22 / 7 x 73
V = 718.67cm3
2) We're given that the width of the canal is 6 m.
The depth of the canal is 1.5 m.
The speed of the water flowing is 4 km / hr = 4000 m / hr.
The length of the water column formed in 10 minutes = 1 / 6 hour = 1 / 6 x 4000 = 666.67 m.
The volume of water flowing in 1/6 of an hour = volume of the cuboid of length 666.67 m, width 6 m and depth 1.5 m.
= 666.67 x 6 x 1.5 = 6000.03 = 6000 m3.
Let x m2 be the area irrigated in 1/6 of an hour, making it:
x * (8 / 100) = 6000
x = 75000 m2.
Work hard for your GCSE Mathematics examination!
End of analysis. Great!
