Sure! Let's go through the problem step by step:
### Volume of the Toy Box
To calculate the volume of a rectangular box, you use the formula:
[tex]\[ \text{Volume} = \text{Height} \times \text{Width} \times \text{Depth} \][/tex]
Given:
- Height = 24 inches
- Width = 36 inches
- Depth = 18 inches
Plugging the values into the formula:
[tex]\[ \text{Volume} = 24 \, \text{inches} \times 36 \, \text{inches} \times 18 \, \text{inches} = 15552 \, \text{cubic inches} \][/tex]
### Surface Area of the Toy Box
To find the surface area of a rectangular box, you use the formula:
[tex]\[ \text{Surface Area} = 2 (\text{Height} \times \text{Width} + \text{Height} \times \text{Depth} + \text{Width} \times \text{Depth}) \][/tex]
Calculating each term first:
- Height × Width = 24 inches × 36 inches = 864 square inches
- Height × Depth = 24 inches × 18 inches = 432 square inches
- Width × Depth = 36 inches × 18 inches = 648 square inches
Summing these up:
[tex]\[ \text{Surface Area} = 2 (864 + 432 + 648) \, \text{square inches} = 2 \times 1944 \, \text{square inches} = 3888 \, \text{square inches} \][/tex]
### Conversion to Square Feet
Since 1 square foot equals 144 square inches, to convert the surface area into square feet, we divide by 144:
[tex]\[ \text{Surface Area in square feet} = \frac{3888 \, \text{square inches}}{144 \, \text{(square inches/square foot)}} = 27 \, \text{square feet} \][/tex]
### Number of Cans of Paint Needed
If each can of paint covers 35 square feet, we calculate the number of cans needed by dividing the total surface area by the coverage per can and then rounding up to the nearest whole number (since you can't buy a fraction of a can):
[tex]\[ \text{Cans Required} = \left\lceil \frac{27 \, \text{square feet}}{35 \, \text{(square feet/can)}} \right\rceil \][/tex]
[tex]\[ \text{Cans Required} = \left\lceil 0.771 \right\rceil = 1 \][/tex]
### Summary
- The volume of the toy box is 15552 cubic inches.
- Malcolm needs to buy 1 can of paint to paint the outside of the toy box.
Let me know if you have any further questions or need clarification on any of these steps!
