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?
Solution:
Given: Herbarium of dimensions 30 cm × 25 cm × 25 cm.
Since the herbarium is a cuboid that is enclosed by six rectangle regions called faces having 12 edges, the area of the glass used to make the herbarium will be equal to the total surface area of the cuboid.
Total surface area of the cuboid = 2(lb + bh + hl)
Let the length, breadth and height of the herbarium are l, b and h respectively.
Length, l = 30 cm
Breadth, b = 25 cm
Height, h = 25 cm
The area of the glass = 2(lb + bh + hl)
= 2 × (30 cm × 25 cm + 25 cm × 25 cm + 25 cm × 30 cm)
= 2 × (750 cm2 + 625 cm2 + 750 cm2)
= 2 × 2125 cm2
= 4250 cm2
Since the herbarium is made entirely of glass panes (including base) held together with tape, the length of the tape which is needed for all the 12 edges will be the same as the sum of the lengths of all the 12 edges.
Length of the tape needed for all the 12 edges = 4(l + b + h)
= 4 × (30 cm + 25 cm + 25 cm)
= 4 × 80 cm
= 320 cm
Thus, the area of the glass is 4250 cm2, and the tape needed for all the 12 edges is 320 cm.
☛ Check: NCERT Solutions for Class 9 Maths Chapter 13
Video Solution:
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?
Class 9 Maths NCERT Solutions Chapter 13 Exercise 13.1 Question 6
Summary:
It is given that there is a small indoor greenhouse (herbarium) which is made entirely of glass panes (including base) held together with tape. It is 30 cm long, 25 cm wide and 25 cm high. We have found that the area of the glass is 4250 cm2 and the tape needed for all the 12 edges is 320 cm.
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