Question

marie built a sand castle that is made of two rectangular prisms. she used one bag of sand. if there are 2,000 cubic inches of sand in a bag of sand, how much sand was left after marie built her sand castle?
choose the correct answer below.
a. 440 in³
b. 578 in³

Explanation:

Step1: Calculate volume of top prism

Volume formula: $V_1 = l \times w \times h$
$V_1 = 7 \times 8 \times 5 = 280$ $\text{in}^3$

Step2: Calculate volume of bottom prism

Volume formula: $V_2 = l \times w \times h$
$V_2 = 16 \times 16 \times 5 = 1280$ $\text{in}^3$

Step3: Total sand used

Add the two volumes: $V_{\text{total}} = V_1 + V_2$
$V_{\text{total}} = 280 + 1280 = 1560$ $\text{in}^3$

Step4: Calculate remaining sand

Subtract used sand from total sand: $V_{\text{left}} = 2000 - V_{\text{total}}$
$V_{\text{left}} = 2000 - 1560 = 440$ $\text{in}^3$

Answer:

A. $440 \text{in}^3$