Question

6. 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.
(Jammu 2019)
(i) What is the surface area of the glass ?
(ii) How much of tape is needed for all the 12 edges ?​

Answer 1

Answer

$\purple{\bigstar}$ Surface area of the glass $\leadsto$ $\boxed{\sf{\red{4250~cm^2}}}$

$\purple{\bigstar}$ Tape needed for all the 12 edges $\leadsto$ $\boxed{\sf{\red{340~cm}}}$

• Given

• Dimensions of a small indoor greenhouse (herbarium) -
• Length of the herbarium = 30 cm
• Breadth of the herbarium = 25 cm
• Height of the herbarium = 25 cm

• To find

• Surface area of the glass
• How much tape is needed for all the 12 edges.

• Solution

$\purple{\bigstar}$ $\boxed{\underline{\sf{Total~surface~area = 2(lb + bh + hl)}}}$

Substitute the given values,

⟶ 2(30 × 25 + 25 × 25 + 25 × 30)

⟶ 2(750 + 625 + 750)

⟶ 2(2125)

⟶ 4250 cm²

• Surface area of the glass = 4250 cm²

The herbarium has 12 edges. So, it is in thr shape of a cuboid.

Therefore,

$\purple{\bigstar}$ $\boxed{\underline{\sf{Length~of~cuboid = 4(l + b+ h)}}}$

Substitute the given values,

⟶ 4(30 + 25 + 30)

⟶ 4(85)

⟶ 340 cm

• Tape needed for all the 12 edges = 340 cm

________________________________

Some related formulae -

• Total Surface Area of cube = 6 × side²
• Lateral Surface Area of cube = 4 × Side²
• Volume of cube = Side³
• Diagonal of a cube = √3l
• Perimeter of cube = 12 × side
• Perimeter of cuboid = 4(l + b + h)
• Total Surface area of cuboid =2(lb + bh + hl)
• Lateral Surface area of cuboid = 2h(l + b)
• Volume of the cuboid = lbh
• Diagonal of the cuboid =√l² + b² + h²

Answer 2

$\huge{\orange{\underline{\underline{Answer:-}}}}$

Given:

Herbarium held together with tape is

Length = l = 30 cm

Breadth = b = 25 cm

Height = 25 cm

To find:

• Surface area of glass = ?
• Tape needed for all 12 edges = ?

Solution:

Herbarium is like cuboid shaped

Surface area of glass = Total Surface area of cuboid

SA = 2 [ lb + bh + lh] ---(SA = surface area)

SA = 2[ 30 × 25 + 25 × 25 + 30 × 25 ]

SA = 2[ 750 + 625 + 750 ]

SA = 2 × 2125

SA = 4250

Surface area of glass is 4250 cm²

In a cuboid, we know there are 12 edges

Note:

So, If we take length, breadth and height there are 4 length, 4 breadth and 4 height. So we should add this length, breadth and height to get tape length. In fact we should find perimeter of cuboid. As perimeter is length of outline or circumference

Tape required = Perimeter of cuboid

= 4l + 4b + 4h

= 4 × 30 + 4 × 25 + 4 × 25

= 120 + 100 + 100

= 320 cm

Answer:

Thus, Surface area of glass is 4250 cm² and tape required for joining 12 edges is 320 cm

Knowledge booster:

⟹ Total surface area of cuboid

= 2 ( lb+bh +lh)

⟹ Volume of cuboid = l × b × h

⟹ Lateral surface area of cuboid

= 2 h(l +b)

⟹ Diagonal of cuboid = √l²+b² + h²

⟹ Perimeter of cuboid = 4( l + b + h) . Try solving more such formula based questions to get good hold on it and for remembering formulas