CH-04-001 · Density bounds for a cylindrical solid

A solid metal cylinder has mass 835 g, radius 2.1 cm and height 6.7 cm. The mass is correct to the nearest gram. Both lengths are correct to the nearest 0.1 cm. Calculate the upper bound for its density, in g/cm³. Give your answer to 3 decimal places.

Bounds: Upper Bound of Cylinder Density ("MeDiVa" & Bounds Table) Booklet p. 39, p. 54 & p. 65

Method

1) Find UB of mass and LB of radius & height

2) Minimum volume V_LB = π(r_LB)²(h_LB)

3) From Bounds table: D_UB = M_UB ÷ V_LB

Worked Example (CH-04-001)

From Bounds Table (p. 65): For Division,

\mathbf{UB = UB \div LB}

and

\mathbf{LB = LB \div UB}

1) Upper mass bound = 835.5 g.

2) Lower radius bound = 2.05 cm; lower height bound = 6.65 cm.

3) Use the lower volume

\pi(2.05)^2(6.65)

4) Divide the upper mass by the lower volume.

5) 9.516 g/cm³

9.516 g/cm³