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165 pagesrevision 46935
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Q8a)i) - We can find the ratio of the sides of the larger triangle to the smaller
one as 12/8 = 1.5. The ratio of the areas would be 1.52, giving 2.25. If the
smaller triangle has area 16, the larger one would have area 16*2.25 = 36
cm2.
a)ii) - The ratio of the volumes would be 1.53 = 3.375. If the smaller prism has
volume 320cm3, the larger one would have volume 320*3.375 = 1080 cm3.
Dividing this by the cross sectional area of the prism, which we already found
to be 36, we would get the height/length of the prism, depending on its
orientation. This is 30 cm.
b) - Since the volumes are equal, we would set the volume of the cylinder as
equal to the volume of the sphere. So pi*62*h = 4(pi*4.53)/3. Using this, we
could then move all the terms except for h to the right hand side, to find h as
3.375 cm.