As shown in the figure, a right circular cone has a height h, a base with a radi
ID: 1525103 • Letter: A
Question
As shown in the figure, a right circular cone has a height h, a base with a radius of r, and a side length s. All three of these quantities (h, r, s) have dimensions of length [L] Determine the overall dimensions of each of the following formulas. Please show your work. Example: If the formula is 1/3 pi r^2 h Solution: Dimensions are [L]^2 which is [L] pi r^2 + pi r s (r^2 + h^2)^1/2 (Raising to the power of 1/2 is the same operation as squareroot pi r^2 + 4pi rs Considering only dimensions, which of the formulas above could potentially be a correct formula for the surface area of the cone? Briefly explain your reasoning.Explanation / Answer
A)
take i) (pi*r^2) + (pi*r*s)
dimensions are [L]^2 + [L*L] = [L]^2
ii) (r^2 + h^2)^(1/2) = {[L]^2 + [L]^2 }^(1/2) = [L]
dimesions are [L]
iii)
(pi*r^2)+(4*pi*r*s) = [L]^2+[L*L] = [L]^2 are the dimensions
B) surface area of the cone has dimensions [L]^2
here i) (pi*r^2) + (pi*r*s) and iii) (pi*r^2)+(4*pi*r*s) has same dimensions of suface area of teh cone
so potentially correct formulas are i) (pi*r^2) + (pi*r*s) and iii) (pi*r^2)+(4*pi*r*s)
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