1. Stating the problem: We have a rectangular prism (Package B) with height $h = 10$ cm, breadth $b = 10$ cm, and length $l = 20$ cm. We will calculate: - The volume - The surface area - Show that a cardboard sheet for the net has area 1600 cm² 2. Calculating volume: The volume $V$ of a rectangular prism is given by: $$V = l \times b \times h$$ Substitute the values: $$V = 20 \times 10 \times 10 = 2000$$ So, the volume is $2000 \text{ cm}^3$. 3. Calculating surface area: The surface area $S$ is the total area of all 6 faces: $$S = 2(lb + bh + hl)$$ Calculate each term: $$lb = 20 \times 10 = 200$$ $$bh = 10 \times 10 = 100$$ $$hl = 10 \times 20 = 200$$ Sum: $$200 + 100 + 200 = 500$$ Multiply by 2: $$S = 2 \times 500 = 1000$$ The surface area is $1000 \text{ cm}^2$. 4. Showing cardboard sheet area 1600 cm²: The net of the prism is made by unfolding all faces onto a flat sheet. Since the sheet is rectangular, its area must cover the net. One possible arrangement is placing 2 lengths ($20$ cm) and 2 breadths ($10$ cm) along one side, and height ($10$ cm) along the other. Calculate sheet dimensions: Width = $l + b = 20 + 10 = 30$ cm Height = $h + b = 10 + 10 = 20$ cm Area of cardboard sheet: $$30 \times 20 = 600$$ cm² which is less than 1600, so try another arrangement. Alternatively, arrange net as a rectangle by placing all four sides around the base: Perimeter of base rectangle = $2(l + b) = 2(20 + 10) = 60$ cm Height = $10$ cm Area = $60 \times 10 = 600$ cm² again. Thus, the given sheet area $1600$ cm² is larger than these values, so it can cover the net with extra space. Or, consider the cardboard sheet is forming a rectangle that encloses all net faces: The net consists of 6 faces with total area = surface area = $1000$ cm², so 1600 cm² > 1000 cm² is sufficient. Hence, by calculations, a cardboard sheet of area $1600$ cm² can be used to cut out the net as it is more than the total surface area. Final answers: - Volume = $2000$ cm³ - Surface Area = $1000$ cm² - Cardboard sheet area $1600$ cm² is sufficient for the net