Victory for the ACT Student Text 15e

242 • M ATH

SOLIDS

26. The prism below has bases with sides of lengths 12, 16, and 20 centimeters. The distance between the bases is 30 centimeters. What is the lateral surface area, in square centimeters, of the prism? F. 1,632 G. 1,440 H. 600 J. 480 K. 360 27. What is the approximate surface area, in square inches, of a ball with a largest circumference of 12 r inches? ( 4 SA r 2 r Sphere )

28. The volume of a cone can be found using the formula 3 1 V r h 2 r . If a cone has a height of 10 cm and a volume of 120 cm r 3 , what is the diameter of its base, in centimeters? F. 6 G. 12 H. 36 J. 72 K. 144 29. A construction company is building a silo. The silo is a cylinder with a hemisphere on top. The diameter of the cylinder is 42 feet and the height of the cylinder is 40 feet. How much hay can be stored in the silo, in cubic feet?

A. 12 r B. 36 r C. 144 r D. 576 r E. 2, 304 r

A. 23, 814 r B. 29, 988 r C. 711, 774 r D. 717, 948 r E. 70,560 + 6, 174 r

Throwback to Math Class Cube volume: V x 3 Cube surface area: SA x 6 2 Prism volume: V = bwh Prism surface area: SA 2 bw Cylinder volume: V r h 2 r Cylinder lateral surface area: 2 LSA rh r Cylinder total surface area: 2 2 TSA rh r = + r r 2 Sphere volume: V r r 3 4 3 Sphere surface area: 4 SA r 2 r + 2 wh + 2 bh

Cube

Prism

Cylinder

Sphere

V r h 2 r 2 LSA rh r 2 2 TSA rh r

3

3 4 V r 3 r

V bwh

V x

2 bw

2 wh

2 bh

SA x 6 2 SA

4 SA r 2 r

2 r r + =