Case Study Based Question on Surface Area and Volume
Tamper-proof tetra-packed milk guarantees both freshness and security. This milk ensures uncompromised quality, preserving the nutritional values within and making it a reliable choice for health-conscious individuals.
500 mL milk is packed in a cuboidal container of dimensions 15cm×8cm×5cm. These milk packets are then packed in cuboidal cartons of dimensions 30cm×32cm×15cm.
Based on the above given information, answer the following questions :
(i) Find the volume of the cuboidal carton. [1 Mark]
(ii) (a) Find the total surface area of a milk packet. [2 Marks]
OR
(b) How many milk packets can be filled in a carton? [2 Marks]
(iii) How much milk can the cup (as shown in figure) hold? [1 Mark]
CBSE 2024
Solution :
Dimensions of cuboidal container
l = 15 cm
b = 8 cm
h = 5 cm
Dimensions of cuboidal cartons
L = 30 cm
B = 32 cm
H = 15 cm
Dimensions of cylindrical cup
r = 5 cm
h'= 7cm
(i) Volume of the cuboidal carton
= LBH
= 30×32×15
= 14400 cm³
(ii)
(a) Total Surface Area of a milk packet
=2(lb+bh+hl)
=2[(15×8)+(8×5)+(5×15)]
=2[120+40+75]
=2[235]
=470 cm²
OR
(b) No. of milk packets filled in a carton
= Volume of carton / Volume of milk packet
= LBH/lbh
= (30×32×15) / (15×8×5)
= 2×4×3
= 24
(iii) Capacity of the cup = Volume of the cylinder
= πr²h
=(22/7)×5×5×7
= 22×25
= 550 cm³