A playground is being redesigned. The first step is to fill in a tunnel that has

Question

A playground is being redesigned. The first step is to fill in a tunnel that has been deemed unsafe. (a) (i) The cylindrical tunnel has diameter 0.80 m and length 4.0 m. What is its volume? (ii) It requires 213 kg of cement to make 1 cubic metre of concrete. How much cement is needed to make the concrete required to fill the tunnel? Give your answer as a whole number of kilograms, rounded appropriately. (b) A circular roundabout is planned, with diameter 2.5 m. (i) The roundabout needs a rubber surface on the circular floor, right to the edges. What is the area of the floor? (ii) The roundabout then needs an edging. What is its circumference? (c) The frame for a swing will be fitted as shown in Figure 2. (This diagram is not drawn to scale.) The horizontal bar CD is 1 m long. Bars CA, CD, DE and DF, all of equal length, form the legs of the frame. The vertical height of the top of the swing, the length CM, is 3 m, and the angle between the sloping bars of the frame and the ground, for example angle ABC, is 70 degree. The point C is vertically above the point M. Find the total length of bars needed to make the frame of the swing.

Explanation / Answer

a) i) d = 0.80 m and length = 4.0 m

volume = pi*r^2*l = pi*(0.8)^2*4 = 8.04 m^3

b) It takes 213 kg of cement to make 1 m^3 of concrete

So, weight of cement = 213*8.04 = 1713.05 =1713kg

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