Q2 A small indoor greenhouse (herbarium) is made entirely of glass panes (including base) held together with tape. It is 30 cm long, 25 cm wide and 25 cm high. (i) What is the area of the glass? (ii) How much of tape is needed for all the 12 edges?
Answers & Comments
shivamchaudhary98707
(i) The area of the glass can be calculated by finding the sum of the areas of each of the six sides of the greenhouse.
Area of one side = length * height Area of one side = 30 cm * 25 cm = 750 square cm
So, the area of all six sides will be 750 * 6 = 4500 square cm.
(ii) To find the amount of tape needed for all 12 edges, we need to calculate the perimeter of all sides and add them together.
Perimeter of a side = 2 * (length + width) Perimeter of a side = 2 * (30 cm + 25 cm) = 110 cm
Since there are six sides, the total perimeter will be 110 cm * 6 = 660 cm.
Therefore, the amount of tape needed for all 12 edges is 660 cm
Answers & Comments
Area of one side = length * height
Area of one side = 30 cm * 25 cm = 750 square cm
So, the area of all six sides will be 750 * 6 = 4500 square cm.
(ii) To find the amount of tape needed for all 12 edges, we need to calculate the perimeter of all sides and add them together.
Perimeter of a side = 2 * (length + width)
Perimeter of a side = 2 * (30 cm + 25 cm) = 110 cm
Since there are six sides, the total perimeter will be 110 cm * 6 = 660 cm.
Therefore, the amount of tape needed for all 12 edges is 660 cm
Answer:
[tex]\sf\:\boxed{\begin{aligned}& \qquad \:\bf \: Area\:of\:glass = 4250 \: {cm}^{2} \qquad \: \\ \\& \qquad \:\bf \: Length\:of\:tape\:required = 320 \: cm \: \qquad \end{aligned}}[/tex]
Step-by-step explanation:
Dimensions of greenhouse (herbarium):
Length of greenhouse, l = 30 cm
Breadth of greenhouse, b = 25 cm
Height of greenhouse, h = 25 cm
Now, area of glass used is equals to total surface area of cuboid which is 30 cm long, 25 cm wide and 25 cm high.
Thus,
[tex]\sf\: Area\:of\:glass \\ [/tex]
[tex]\sf\: = \: 2(lb + bh + hl) \\ [/tex]
[tex]\sf\: = \: 2(30 \times 25 + 25 \times 25 + 25 \times 30) \\ [/tex]
[tex]\sf\: = \: 2(750 + 625 + 750) \\ [/tex]
[tex]\sf\: = \: 2 \times 2125 \\ [/tex]
[tex]\sf\: = \: 4250 \: {cm}^{2} \\ [/tex]
Thus,
[tex]\implies\sf\:\boxed{\sf\: Area\:of\:glass \: = \: 4250 \: {cm}^{2} \: } \\ [/tex]
Now, we have to find how much of tape is needed for all the 12 edges. So, greenhouse has 4 length, 4 breadth and 4 height as 12 edges. So,
[tex]\sf\: Length\:of\:tape\:required \\ [/tex]
[tex]\sf\: = \: 4(l + b + h) \\ [/tex]
[tex]\sf\: = \: 4(30 + 25 + 25) \\ [/tex]
[tex]\sf\: = \: 4 \times 80 \\ [/tex]
[tex]\sf\: = \: 320 \: cm \\ [/tex]
Thus,
[tex]\implies\sf\:\boxed{\sf\:Length\:of\:tape\:required \: = \: 320 \: cm \: } \\ [/tex]
Hence,
[tex]\implies\sf\:\sf\:\boxed{\begin{aligned}& \qquad \:\bf \: Area\:of\:glass = 4250 \: {cm}^{2} \qquad \: \\ \\& \qquad \:\bf \: Length\:of\:tape\:required = 320 \: cm \: \qquad \end{aligned}}[/tex]