**GCSE** **Mathematics**** Question Analysis Topic: Mathematics - Short Questions**

**Exam Questions:**

1) If the total surface area of a solid hemisphere is 462 cm^{2}, 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 cm**^{2}, from 2πr^{2}.

> 462 = 3πr^{2}

> **r = 7 cm**.

The volume of the hemisphere is 2/3 x πr^{3}.

so V = 2 / 3 x 22 / 7 x 7^{3}**V = 718.67cm**^{3}

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 m**^{3}.

Let x m^{2} be the area irrigated in 1/6 of an hour, making it:

x * (8 / 100) = 6000

x = **75000 m**^{2}.

Work hard for your GCSE Mathematics examination!

End of analysis. Great!