Problem Set: Measuring Volume & Length 1. Suppose a cylindrical container has the following dimensions: Height = 14.93 cm Diameter = 4.45 cm

and jellybeans in the container have the following dimensions: Height = 9.9 mm Length = 13.9 mm Width = 5.5 mm How many jellybeans fit inside the container? Express your answer in scientific notation and with the appropriate number of significant figures. Volume of a jellybean: 760 mm3 or 0.76 cm3 (2 significant figures) Volume of container: 232 cm3 or 232,000 mm3 (3 significant figures) Number of jellybeans in container: 3.0 x 102 (2 significant figures) Note: To determine the number of jellybeans, the units for the volume of a jellybean and the container must be the same. 2. Using a ruler measure the width and length of the rectangle below. Determine the area of the rectangle in cm

2 (significant figures and scientific notation)

2.25 cm x 12.07 cm = 27.2 cm2 = 2.72 x 101 cm2

Determine the area of the rectangle in mm

2 (significant figures and scientific notation)

22.5 mm x 120.7 mm = 2720 mm2 = 2.72 x 103 mm2

Determine the area of the rectangle in m

2 (significant figures and scientific notation)

0.0225 m x 0.1207 m = 0.00272 m2 = 2.72 x 10-3 m2

3. A standard sheet of 8 1/2’’ x 11 ” (21.50 cm x 28.00 cm) paper can be made into a cylinder two ways: A) where length of the cylinder is 8 ½ inches (21.50 cm) and its circumference is 11 inches (28.00 cm) B) where the length of the cylinder is 11 inches (28.00 cm) and its circumference is 8 ½ inches (21.50 cm) • Determine the volume of each cylinder to determine which cylinder has the greater volume. • Express your answer in scientific notation and with the appropriate number of significant figures.

Circumference = 2 π r Volume = π r2 h Cylinder A: radius = C / 2 π = 28.00 cm / 2 π = 4.459 cm

Volume = π r2 h = π x (4.459 cm)2 x 21.50 cm = 1342 cm3 or 1.342 x 103 cm3 Cylinder B: radius = C / 2 π = 21.50 cm / 2 π = 3.424 cm

Volume = π r2 h = π x (3.424 cm)2 x 28.00 cm = 1031 cm 3 or 1.031 x 103 cm 3 The container with the larger circumference (radius) has the greater volume.

A B