AMC8 2002

AMC8 2002 · Q13

AMC8 2002 · Q13. It mainly tests 3D geometry (volume).

For his birthday, Bert gets a box that holds 125 jellybeans when filled to capacity. A few weeks later, Carrie gets a larger box full of jellybeans. Her box is twice as high, twice as wide and twice as long as Bert's. Approximately, how many jellybeans did Carrie get?

伯特生日时得到一个满载时可容纳125颗果冻豆的盒子。几周后，嘉莉得到一个更大的满载果冻豆的盒子。她的盒子高度、宽度和长度都是伯特的盒子的两倍。大约，嘉莉得到了多少颗果冻豆？

(A) 250 250

(B) 500 500

(D) 750 750

(E) 1000 1000

Answer

Correct choice: (E)

正确答案：（E）

Solution

Since the exact dimensions of Bert's box do not matter, assume the box is $1 \times 2 \times 3$. Its volume is 6. Carrie's box is $2 \times 4 \times 6$, so its volume is 48 or 8 times the volume of Bert's box. Carrie has approximately $8(125) = 1000$ jellybeans.

由于伯特盒子的确切尺寸无关紧要，假设盒子为$1 \times 2 \times 3$。其体积为6。嘉莉的盒子为$2 \times 4 \times 6$，体积为48，即伯特盒子体积的8倍。嘉莉大约有$8(125) = 1000$颗果冻豆。

Topics

GE.013 3D geometry (volume)