If a cross section of the paperweight is cut perpendicular to the base but does not pass through the top vertex, which shape des
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A dimension of a sphere is its radius, so it correlates with its volume, thus
![\bf \cfrac{\textit{similar shape}}{\textit{similar shape}}\qquad \cfrac{s}{s}=\cfrac{\sqrt{s^2}}{\sqrt{s^2}}=\cfrac{\sqrt[3]{s^3}}{\sqrt[3]{s^3}}\\\\ -------------------------------\\\\ %The volume of two spheres are 327\pi in^{3} and 8829\pi in^{3} \cfrac{small}{large}\qquad \cfrac{s}{s}=\cfrac{\sqrt[3]{s^3}}{\sqrt[3]{s^3}}\implies \cfrac{s}{s}=\cfrac{\sqrt[3]{327}}{\sqrt[3]{8829}}\qquad \begin{cases} 8829=3\cdot 3\cdot 3\cdot 327\\ \qquad 3^3\cdot 327 \end{cases}](https://tex.z-dn.net/?f=%5Cbf%20%5Ccfrac%7B%5Ctextit%7Bsimilar%20shape%7D%7D%7B%5Ctextit%7Bsimilar%20shape%7D%7D%5Cqquad%20%5Ccfrac%7Bs%7D%7Bs%7D%3D%5Ccfrac%7B%5Csqrt%7Bs%5E2%7D%7D%7B%5Csqrt%7Bs%5E2%7D%7D%3D%5Ccfrac%7B%5Csqrt%5B3%5D%7Bs%5E3%7D%7D%7B%5Csqrt%5B3%5D%7Bs%5E3%7D%7D%5C%5C%5C%5C%0A-------------------------------%5C%5C%5C%5C%0A%25The%20volume%20of%20two%20spheres%20are%20327%5Cpi%20in%5E%7B3%7D%20and%208829%5Cpi%20in%5E%7B3%7D%0A%5Ccfrac%7Bsmall%7D%7Blarge%7D%5Cqquad%20%5Ccfrac%7Bs%7D%7Bs%7D%3D%5Ccfrac%7B%5Csqrt%5B3%5D%7Bs%5E3%7D%7D%7B%5Csqrt%5B3%5D%7Bs%5E3%7D%7D%5Cimplies%20%5Ccfrac%7Bs%7D%7Bs%7D%3D%5Ccfrac%7B%5Csqrt%5B3%5D%7B327%7D%7D%7B%5Csqrt%5B3%5D%7B8829%7D%7D%5Cqquad%20%0A%5Cbegin%7Bcases%7D%0A8829%3D3%5Ccdot%203%5Ccdot%203%5Ccdot%20327%5C%5C%0A%5Cqquad%203%5E3%5Ccdot%20327%0A%5Cend%7Bcases%7D)
![\bf \cfrac{s}{s}=\cfrac{\sqrt[3]{327}}{\sqrt[3]{3^3\cdot 327}}\implies \cfrac{s}{s}=\cfrac{\underline{\sqrt[3]{327}}}{3\underline{\sqrt[3]{327}}}\implies \cfrac{s}{s}=\cfrac{1}{3}](https://tex.z-dn.net/?f=%5Cbf%20%5Ccfrac%7Bs%7D%7Bs%7D%3D%5Ccfrac%7B%5Csqrt%5B3%5D%7B327%7D%7D%7B%5Csqrt%5B3%5D%7B3%5E3%5Ccdot%20327%7D%7D%5Cimplies%20%5Ccfrac%7Bs%7D%7Bs%7D%3D%5Ccfrac%7B%5Cunderline%7B%5Csqrt%5B3%5D%7B327%7D%7D%7D%7B3%5Cunderline%7B%5Csqrt%5B3%5D%7B327%7D%7D%7D%5Cimplies%20%5Ccfrac%7Bs%7D%7Bs%7D%3D%5Ccfrac%7B1%7D%7B3%7D)
Answer : 2 4/5 grams.
Hope this helps. - M