you are trying to find the volume a regular tetrahedron (shown below). you know that by construction, all…

you are trying to find the volume a regular tetrahedron (shown below). you know that by construction, all the edges have the same length, which you measure to be 30 cm, with possible error of 0.3 cm. use differentials to estimate the maximum possible error when computing the volume of the tetrahedron if the volume of a regular tetrahedron is $v = \\frac{e^{3}}{6\\sqrt{2}}$, where e is the length of each edge. your answer will be of the form $\\frac{b}{\\sqrt{2}} cm^{3}$, where b is some fraction or integer. find b. $b =$ number (3 significant figures)

you are trying to find the volume a regular tetrahedron (shown below). you know that by construction, all the edges have the same length, which you measure to be 30 cm, with possible error of 0.3 cm. use differentials to estimate the maximum possible error when computing the volume of the tetrahedron if the volume of a regular tetrahedron is $v = \\frac{e^{3}}{6\\sqrt{2}}$, where e is the length of each edge. your answer will be of the form $\\frac{b}{\\sqrt{2}} cm^{3}$, where b is some fraction or integer. find b. $b =$ number (3 significant figures)

Answer

Explanation:

Step1: Find the derivative of (V) with respect to (e)

Given (V=\frac{e^{3}}{6\sqrt{2}}), using the power rule ((x^{n})^\prime = nx^{n - 1}), we have (dV=\frac{3e^{2}}{6\sqrt{2}}de=\frac{e^{2}}{2\sqrt{2}}de).

Step2: Substitute (e = 30) and (de=0.3) into the differential formula

Substitute (e = 30) and (de = 0.3) into (dV=\frac{e^{2}}{2\sqrt{2}}de). Then (dV=\frac{30^{2}\times0.3}{2\sqrt{2}}). First, calculate (30^{2}\times0.3=(900)\times0.3 = 270). Then (\frac{270}{2\sqrt{2}}=\frac{135}{\sqrt{2}}).

Answer:

(135)