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Problem 1. Frustum of a right circular cone. The volume of a frustum of a right circular cone (see figure on the right) is given by V = πh(R² +rR+r²). Show that the volume uncertainty is given by SV = Vo 2 [(sh) ² + (2 Ro + ro)² (6R)² + (Ro + 2ro)² (6r)²211¹/2 ho (R² + ro Ro + ²)² R- h

Problem 1. Frustum of a right circular cone. The volume of a frustum of a right circular cone (see figure on the right) is given by V = πh(R² +rR+r²). Show that the volume uncertainty is given by SV = Vo 2 [(sh) ² + (2 Ro + ro)² (6R)² + (Ro + 2ro)² (6r)²211¹/2 ho (R² + ro Ro + ²)² R- h

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TOPIC: UNCERTAINTY 

Solve the problem and show the step by step solution. You can use the table for reference/guide.

OPERATION Addition z = x + y Subtraction 2= x - y Multiplication by constant z = cx, (c = const.) Product z = xy Quotient = x/y 2= Raising to a power 2=xn General function of x = f(x) General function of x & y = f(x,y) 2 BEST ESTIMATE 20 = xo + Yo Zoo Yo 20 = Cx0 Zo= xoyo 20 = zo = xo хо Yo 20 = = f(xo) 2 = = f(xo, yo) dz UNCERTAINTY dz= = dz 201 dz= √(6x)² + (dy)² 82 201 /(8x)² + (dy)² dz af əx dz = cdx 2 dx (SH) ². dx xo 10 Oz = nah-18x df (xo) dx dx 2 2 + + -dx + Yo dy Yo 2 2 af (of 10 ду dy
Transcribed Image Text:OPERATION Addition z = x + y Subtraction 2= x - y Multiplication by constant z = cx, (c = const.) Product z = xy Quotient = x/y 2= Raising to a power 2=xn General function of x = f(x) General function of x & y = f(x,y) 2 BEST ESTIMATE 20 = xo + Yo Zoo Yo 20 = Cx0 Zo= xoyo 20 = zo = xo хо Yo 20 = = f(xo) 2 = = f(xo, yo) dz UNCERTAINTY dz= = dz 201 dz= √(6x)² + (dy)² 82 201 /(8x)² + (dy)² dz af əx dz = cdx 2 dx (SH) ². dx xo 10 Oz = nah-18x df (xo) dx dx 2 2 + + -dx + Yo dy Yo 2 2 af (of 10 ду dy
Problem 1. Frustum of a right circular cone. The volume of a frustum of a right circular cone (see figure on the right) is given by V = πh(R² +rR+r²). Show that the volume uncertainty is given by SV = Vo 2 [(sh) ² + (2 Ro + ro)² (6R)² + (Ro + 2ro)² (6r)²11¹/2 ho (R² + ro Ro + ²)² -R- h
Transcribed Image Text:Problem 1. Frustum of a right circular cone. The volume of a frustum of a right circular cone (see figure on the right) is given by V = πh(R² +rR+r²). Show that the volume uncertainty is given by SV = Vo 2 [(sh) ² + (2 Ro + ro)² (6R)² + (Ro + 2ro)² (6r)²11¹/2 ho (R² + ro Ro + ²)² -R- h
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