AMC10 2020 B

AMC10 2020 B · Q2

AMC10 2020 B · Q2. It mainly tests 3D geometry (volume).

Carl has 5 cubes each having side length 1, and Kate has 5 cubes each having side length 2. What is the total volume of these 10 cubes?

Carl 有 5 个边长为 1 的立方体，Kate 有 5 个边长为 2 的立方体。这些 10 个立方体的总体积是多少？

(A) 24 24

(B) 25 25

(D) 40 40

(E) 45 45

Answer

Correct choice: (E)

正确答案：（E）

Solution

The volume of each of the cubes of side length 1 is $1^3 = 1$. The volume of each of the cubes of side length 2 is $2^3 = 8$. Because there are 5 cubes of each type, the sum of the volumes is $5(1+8) = 45$.

边长为 1 的每个立方体的体积是 $1^3 = 1$。边长为 2 的每个立方体的体积是 $2^3 = 8$。因为每种有 5 个立方体，总体积是 $5(1+8) = 45$。

Topics

GE.013 3D geometry (volume)