Question

A sculptor plans to ship the pyramid shown in one of three boxes. The interior of the pyramid holds 4,500 cm3 of water. The base is an isosceles trapezoid. Into which boxes will the pyramid fit? Drag “yes” or “no” to each box height.

Answer 1

Area of base

• 1/2(30+20)(20)
• 10(50)
• 500cm²

Volume=1/3Area×Height

Height

• 4500(3)(500)
• 27cm

So answers are

boxes of 28cm and 32cn

Answer 2

• 28 cm and 32 cm

Explanation:

Volume of the pyramid:

• V = 1/3Bh

Find base area:

• B = 1/2(20 + 30)*20 = 500 cm²

Substitute value of the volume and find the height of the pyramid:

• 4500 = 1/3*500*h
• h = 4500*3/500
• h = 27 cm

The boxes with h > 27 can fit the pyramid:

• 28 cm and 32 cm