The base of a prism is a rectangle whose length is twice its width. The perimeter of the base is 30 cm. The prism's height decreases in an arithmetic progression from 15 cm in the first layer to 9 cm in the fourth layer. What is the total volume of the prism?
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. 2400 cm3.
Base rectangle: Length = 2 × Width, and Perimeter = 30 cm
Let Length = l and Width = w
l = 2w
Perimeter = 2(l + w) = 30
⇒ l + w = 15
⇒ 2w + w = 15
⇒ 3w = 15
⇒ w = 5
⇒ l = 2 × 5 = 10
Base area = 10 × 5 = 50 cm2
Heights: 15 cm, 13 cm, 11 cm, 9 cm
Total height = 15 + 13 + 11 + 9 = 48 cm
Volume = Base area × Total height
= 50 × 48
= 2400 cm3