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mathematicsprinted 95 · PDF 96
165 pagesrevision 46935
printed 95 · PDF 96
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Q5a)i) - The radius is half of the diameter, so if d = 8 cm, r = 4 cm. This can
be directly plugged into the given formula with the height to give a volume of
251 cm. (Final answer should be given in 3 s.f.)
a)ii) - The slant height, also known as l, would be the hypotenuse of the
triangle with base r, and height h. So in this case, with r = 4 and h = 15, l
would be the root of the sum of the squares of 4 and 15, giving l = root of 241.
This can be plugged into the formula for curved surface area to give it as
195.08. The total area is this curved area summed with the base area which is
simply the circle base’s area, which is pi into the radius squared. This gives a
final area of 79.5 cm2.
b)i) - 300 litres can be multiplied by 1000 millilitres per litre to give 300,000
millilitres. Dividing this by 375 millilitres per second, we get 800 seconds,
which when divided by 60, gives 13.33 minutes. 13 minutes is 780 seconds,
so the remainder is 20 seconds. Thus, the time taken to fill the container is 13
mins and 20 secs.
b)ii) - The volume V is 300 litres, which is 300,000 millilitres, which is 300,000
cubic centimetres. This can be divided by 100^3 cm^3 per m^3 to give 0.3
cubic metres as the final volume. Using the formula for volume of a cylinder,
and plugging in r, we can find h to be approximately 0.472 metres.