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\fA barrel is shaped like an ellipsoid with equal pieces cut from the ends by planes perpendicular to the zeaxis, The crossesections perpendicular to the zeaxis are circular The barrel is 2h units high, its midsectiori radius is R: and its end radii are both r Find a formula for the barrels volume Then check two things. First' suppose the Sides ofthe barrel are straightened to turn the barrel into a cylinder of radius R and height 2h Check to see if your formula gives the cylinder's volume Second, suppose r: 0 and h : R so the barrel is a sphere Check to see if yourformula give the spheres volume E] Click the icon to View a picture of the barrel. 2 2 2 x Find a formula for the barrel's volume Assume the equation of the original ellipsOid to be i + i + 2 21 a b2 [:2 Volume = Picture of the barrel Below is a picture ofthe barrel in the problem statement, Use a GAS to plot the surface Identify the type of quadric surface from your graph. 8x2 =22 3y2 Choose the best graph of the equation below. Q A. U B. C: c. A line passes through the points P( - 2,2, - 3) and Q( - 5,4,2). Find the standard parametric equations for the line, written using the base point P( - 2,2, - 3) and the components of the vector PQ. - . . Let z = - 3 + 5t. x = ], y=]. z=0 (Type expressions using t as the variable.)Find parametric equations for the line through (6, - 4,7) parallel to the x-axis. Let z = 7. X= y = Z= - 00