Question

The total surface area of a cuboid is 846 cm. Find the volume if the dimensions are proportional at
5:4:3.
(a) 1500 cm^3 (b) 1620 cm^3(c) 1260 cm^3 (d) 1320 cm^3​

Answer 1

SOLUTION:-

Given:

•The total surface area of a cuboid=846cm.

•The dimensions are proportional at 5:4:3.

To find:

The volume of the cuboid.

Explanation:

Assume length be 5R cm breadth be 4R cm height be 3R cm of the block.

Formula of the total surface area of the cuboid;

=) 2(lb+bh+lh) sq. units.

According to the question:

=) 2(5R ×4R +4R ×3R + 5R ×3R)= 846

=) 2 (20R² + 12R² + 15R²) = 846

=) 2(47R²) = 846

=) 94R² = 846

=) R² = 846/94

=) R² = 9

=) R= √9

=) R= 3

Now,

•Length= 5R =(5×3)cm = 15cm.

•Breadth= 4R = (4×3)cm= 12cm.

•Height = 3R = (3×3)cm= 9cm.

Volume of the cuboid = lbh cu

=) 15cm × 12cm ×9cm

=) 1620cm³

Option (b)✓

Hope it helps ☺️