A rock is submerged in a rectangular prism whose base measures 9cm by 15 cm. If the water level rises from a height of 8cm to 12cm. What is the volume of the rock?
What I did:
V= area of base× height of prism L×W×h
9cm×15cm= 135
8cm×12cm= 96
(I'm not sure what I am supposed to do now. I know you have to subracat the volume of rectabgular prism by the water level rising, but I'm confused on how to do it)
Most direct way:
The volume of the rock equals the change in the volume of the tank.
The change in the height was 4 cm.
So the volume of the rock is (9)(15)(4) cm^3
= 540 cm^3
or, along your thinking
volume of tank at the start
= (9)(15)(8) or 1080 cm^3
volume after rock is inserted
= (9)(15)(12) or 1620 cm^3
change in volume caused by the rock
= 1620 cm^3 - 1080 cm^3
= 540 cm^3 , as above
To find the volume of the rock, you need to subtract the volume of the rectangular prism after the water level has risen from the initial volume of the rectangular prism.
The initial volume of the rectangular prism can be calculated using the equation V = length × width × height:
V_initial = 9 cm × 15 cm × 8 cm
V_initial = 1080 cm^3
Now, we need to find the volume of the rectangular prism after the water level has risen to 12 cm. We can use the same formula as before:
V_final = 9 cm × 15 cm × 12 cm
V_final = 1620 cm^3
To find the volume of the rock, we subtract the initial volume from the final volume:
V_rock = V_final - V_initial
V_rock = 1620 cm^3 - 1080 cm^3
V_rock = 540 cm^3
Therefore, the volume of the rock is 540 cm^3.