Question
Two similar solids A and B are shown. Solid A has a volume of 60cm^3 a) Work out the volume of solid B. Solid B has a total surface area of 140cm^2 b) Work out the total surface area of solid A
Answer
4.3
(235 Votes)
Nolan
Expert · Tutor for 3 years
Answer
Sure, let's consider the given problem here.(a) In case of Volume: You have two similar solids, which means the ratio of their corresponding sides forms a constant ratio. The volume (V) of any solid in 3D space is proportional to the cube of its sides. Let r be the ratio of the sides of solid B to A, which means the cube of r, that is r³, will be the predicting factor for the volume of Solid B. Mathematically, we can represent this as: V_B = (r³) * V_AFirst, here we need to solve for r, which we can obtain from the data given for the corresponding surface areas. (b) The surface area (SA) of any solid in 3D space is proportional to the square of its sides.Again, I keep it clear—applying the knowledge of similar figures brings about the conclusion, which refers that the surface area (SA) of identical figures is found using the square of their corresponding side lengths, herewith the following expression seems to be adequate:SA_B = (r²) * SA_AThe known provided surface area of Solid B gives me the ability to find r². Now, as you can see here, I have initiated the solution to the problem, but the issue is I still don't have enough information directly. Usually, in problems related to similar solid volumes, and/or areas the ratio is provided or could explicitly be derived.Nonetheless, we can still complete our answer as - the ratios of the volumes V_B and V_A, and total surface areas SA_A and SA_B would be the cube and the square of the ratios of the linear dimensions ("\emph{r}") consequential on taking a positive nth root of these values, respectively but if only these values appear. Final Conversion. (a) Volume of Solid B = ??? We don't have enough information to solve this problem.(b) Total Surface Area of Solid A = ???We don't have an adequate amount of data to solve this problem.Reminder. The availability of the ratio could equip us with the capacity to find this ratio, and then consequently the asked volume and surface area. [Brief for user]: Generally, in such problems, we get hold of a known ratio. If that could't be reached, then we can't merely solve this particular mathematical problem - lacking insufficient data precislely comes up here as a fatal shortfall. Can you check yet again whether any depth about the proportions/ratios is getting missed? Can it be accepted? The equations I proposed above stand out. But regrettably, I couldn't solve the one made by \emph{me} devoid of the proportion of sides/ratio omitted vague. Should there appear the mentioned necessary ratio data display, the precise compact answer is ought to be constructed. Consequentially, having a highlighted computed plain result with no numbers directly can't be given as we are desirous to have an archetypal raw ratio probability offering the solution to a concerned casing/configuration.