A decorative column is made in the shape of a regular hexagonal prism. The side length of its base is 10 cm. The column is built from multiple sections, and their heights form an arithmetic progression: the first section is 5 cm tall, and each subsequent section is 2 cm taller than the previous one. If the column has 4 sections in total, what is the total volume of the column?
Show answer & explanation
Correct answer: B
Explanation
The correct answer is Option 2 i.e. cm3.
Base area of regular hexagon = (3√3)/2 × Side2
Side = 10 cm
Area = (3√3)/2 × 102 = 150√3 cm2
Heights: 5 cm, 7 cm, 9 cm, and 11 cm
Volume = Base area × Height
Volume for 5 cm height = 150√3 × 5 = 750√3 cm3
Volume for 7 cm height = 150√3 × 7 = 1050√3 cm3
Volume for 9 cm height = 150√3 × 9 = 1350√3 cm3
Volume for 11 cm height = 150√3 × 11 = 1650√3 cm3
Total volume = 750√3 + 1050√3 + 1350√3 + 1650√3 = 4800√3 cm3