Surface area and volume examples with solutions

Example 1: Cuboid

Problem: A box is in the shape of a cuboid. Its length is 12 cm, breadth is 10 cm, and height is 8 cm. Find its Total Surface Area (TSA) and Volume.

Solution:

Given: length (l) = 12 cm, breadth (b) = 10 cm, height (h) = 8 cm

1. Volume of the Cuboid:

• Formula:Volume = l × b × h
• Volume = 12 cm × 10 cm × 8 cm
• Volume = 120 cm² × 8 cm
• Volume = 960 cm³

2. Total Surface Area (TSA) of the Cuboid:

• Formula:TSA = 2 × (lb + bh + lh)
• TSA = 2 × ( (12 × 10) + (10 × 8) + (12 × 8) )
• TSA = 2 × ( 120 + 80 + 96 )
• TSA = 2 × ( 296 )
• TSA = 592 cm²

Example 2: Cylinder

Problem: A cylindrical water tank has a radius of 7 meters and a height of 5 meters. Find its Volume and Total Surface Area. (Use π = 22/7)

Solution:

Given: radius (r) = 7 m, height (h) = 5 m

1. Volume of the Cylinder:

• Formula:Volume = πr2h
• Volume = (22/7) × 7² × 5
• Volume = (22/7) × 49 × 5
• Volume = 22 × 7 × 5
• Volume = 154 × 5
• Volume = 770 m³

2. Total Surface Area (TSA) of the Cylinder:

• Formula:TSA = 2πr(r + h)
• TSA = 2 × (22/7) × 7 × (7 + 5)
• TSA = 2 × 22 × 12
• TSA = 44 × 12
• TSA = 528 m²