At 20°C, a brass cube has an edge length of 34 cm. What is the increase in the cube's surface area when it is heated from 20°C to 67°C?

You need the expansion coefficient for brass. Then it's just original distance times expansion coef times temp change = new distance.

Quick

To find the increase in the cube's surface area when it is heated, we need to calculate the initial surface area and the final surface area at the given temperatures. Here's how you can do it:

Step 1: Calculate the initial surface area of the brass cube at 20°C.
The surface area of a cube is given by the formula: 6 * (edge length)^2.
In this case, the edge length is given as 34 cm.
So, the initial surface area at 20°C is: 6 * (34 cm)^2.

Step 2: Calculate the final surface area of the brass cube at 67°C.
To calculate the final surface area when heated, we need to account for the expansion of the cube due to temperature increase.
The coefficient of linear expansion for brass is typically given as approximately 19 x 10^-6 per °C.
To find the change in length, we multiply the coefficient of linear expansion by the initial length of the cube and the change in temperature: ΔL = α * L * ΔT.
In this case, the change in temperature is (67°C - 20°C) = 47°C.

Since the cube has equal side lengths, the change in length is the same for all edges.
So, the final length of each edge is the initial length plus the change in length: Final Length = Initial Length + ΔL = 34 cm + (α * 34 cm * ΔT).

Now we can find the final surface area using the formula: 6 * (Final Length)^2.

Step 3: Calculate the increase in surface area.
Finally, we subtract the initial surface area from the final surface area to find the increase: Increase in Surface Area = Final Surface Area - Initial Surface Area.

By following these steps, you can calculate the increase in the cube's surface area when heated from 20°C to 67°C.