1. A donkey is tied with a rope to a post which is 15 m from a fence. If the length of the rope between the donkey and the post is 17m, calculate the length of the fence within the reach of the donkey.
2. The base of a right pyramid with vertex, V, is a square, PQRS, of side 15 cm. If the slant height is 32 cm long:
3. represent the information in a diagram;
4. calculate its:
5. height, correct to one decimal place;
6. volume, correct to the nearest \(cm^3\)
Explanation
(a) first is to sketch the diagram
Using Pythagoras theorem, x\(^2\) = 17\(^2\) - 15\(^2\) = 64 and x = 8 m. Then, multiplying by 2 we have 16m as the length of the fence within the reach of the donkey.
(b)(i)
PR = \(\sqrt{15^2 + 15^2}\) = 21.2132 cm and PO = OR = \(\frac{21.2132}{2}\) = 10.61 cm.
Then height of the pyramid is 32\(^2\) = h\(^2\) + (10.6066)\(^2\) and h yields h = 30.2 cm.
(b)(ii) Volume = \(\frac{1}{3}\) x 15 x 15 x 30.19106 = 2264 cm\(^2\) (correct to the nearest cm\(^3\)).