A cuboidal box has each edge 10cm and another cuboidal box is 12.5cm long, 10cm wide and 8 cm high. (1) which box has greater layeral surface area and by how much ? (2) which box has the smaller total surface area and by how much ?
Answers
Answer:
a)edge of boxA=10cm
length of boxB=12.5cm
breadth of boxB=10cm
height of boxB=8cm
lateral surface area 9f box A=4*edge
=4*10=40cm^2
lateral surface area of box B=2(L+B)H
=2(12.5+10)8
=360cm^2
box B has greater lateral surface area
b)toatal surface area of box A=6a
=6*10=60cm^2
total surface area of box=2(LB+BH+LH)
=2(125+80+100)
=2*305
=610cm^2
Given :–
- Each edge of Cuboidal box = 10cm.
- Another Cuboidal box = 12.5cm long.
- Width = 10cm.
- Height = 8cm high.
To Find :–
- Which box has greater lateral surface area and by how much ?
- Which box has the smaller total surface area and by how much ?
Solution :–
For Cuboidal box with edge (a) = 10cm.
L.S.A. (lateral surface area) = 4a²
= 4 × 10²
= 4 × 100
= 400cm²
T.S.A. (total surface area) = 6a²
= 6 × 10²
= 6 × 100
= 600cm²
For the Cuboidal box with dimensions,
- Length (l) = 12.5cm
- Breadth (b) = 10cm
- Height (h) = 8cm
∴ L.S.A. = 2 [l + b] × h
= 2 [12.5 + 10] × 8
= 360cm²
T.S.A. = 2[lb + bh + hl]
= 2 [(12.5 × 10) + (10 × 8) + (8 × 12.5)]
= 2 [125 + 80 + 100]
= 2 [305]
= 610cm²
1. A Cuboidal box has the greater lateral surface area by (400 - 360)cm²
= 40cm²
2. T.S.A. of a cubical box is smaller than the Cuboidal box by (610 - 600)cm²
= 10cm²