Let's address each question step by step:
1. **Total Surface Area of Walls:**
1. **Total Surface Area of Walls:**
- Room dimensions: 10' x 20' with 8-foot ceilings.
- Calculated the total surface area of walls as 480 square feet, considering four walls.
2. **Total Volume of the Room:**
- Same room dimensions with an 8-foot ceiling.
- Calculated the total volume, including the closet, as 1600 cubic feet.
The total surface area of the walls can be calculated by finding the area of each wall and then adding them together. For a rectangular room with dimensions 10' x 20' and an 8-foot ceiling, there are four walls.
The walls with dimensions 10' x 8' (two of them) and the walls with dimensions 20' x 8' (two of them).
Let's calculate:
\[ \text{Area of one 10' x 8' wall} = 10 \times 8 = 80 \text{ square feet} \]
\[ \text{Area of one 20' x 8' wall} = 20 \times 8 = 160 \text{ square feet} \]
Now, sum the areas of all four walls:
\[ \text{Total Surface Area} = 2 \times (\text{Area of 10' x 8' wall}) + 2 \times (\text{Area of 20' x 8' wall}) \]
\[ \text{Total Surface Area} = 2 \times 80 + 2 \times 160 \]
\[ \text{Total Surface Area} = 160 + 320 \]
\[ \text{Total Surface Area} = 480 \text{ square feet} \]
So, the total surface area of the walls is 480 square feet.
2. Total Volume of the Room:
The volume of the room can be found by multiplying the length, width, and height. Since the room has an 8-foot ceiling, the volume is:
\[ \text{Volume} = \text{Area of base} \times \text{Height} \]
\[ \text{Volume} = 10 \times 20 \times 8 \]
\[ \text{Volume} = 1600 \text{ cubic feet} \]
So, the total volume of the room, including its closet, is 1600 cubic feet.
The probable question may be:
1. Painters use surface area to determine how much paint they need to buy. Most homes have 8-foot ceilings. Suppose you're going to paint the walls in a room on which you based your drawing. Determine the total surface area of the walls to be painted. Include the walls in the closets, but ignore windows and doors. Round your answer to the hundredths place. Also show all of your calculations and label them appropriately for which room they represent, etc.
The bedroom is 10' x 20' - No closets
2. Choose a bedroom in your drawing. Find the total volume of the room, including its closet. Remember, most homes have 8-foot ceilings.
The bedroom is 10' x 20' - No closets