Question

The volume of a cuboidal block of silver is 10,368cm2. If its dimensions are in the ratio 3:2:1, find : (i) Dimension of the block. (ii) Cost of gold polishing its entire surface at Rs 0.50 per cm2

Answer 1

Given:-

• Volume of cuboidal block = 10368cm²
• Dimensions in ratio = 3:2:1
• Cost of gold polishing its entire surface is at Rs 0.50 per cm².

Solution:-

(i) Let the ratio be x, the. dimensions of block will be 3x:2x:1.

Volume of cuboidal block = 10368cm²

⇒ 6x³ = 10368

$\sf \longmapsto \: 6x = \sqrt[3]{10368} \\ \\ \sf\longmapsto \: x = \sqrt[3]{ \frac{10368}{6} } \\ \\ \sf\longmapsto \: \boxed{ \bf \: x = 12}$

Then, dimensions are:

• 3x = 3(12) = 36
• 2x = 2(12) = 24
• x = 12

(ii) TSA of cuboidal block = 2(lb+bh+hl)

= 2(36×24 + 24×12 + 12×36)

= 3168cm²

Total cost of gold polishing = 3168 × 0.50 = Rs. 1584cm.

Answer 2

Answer:

✯ Given :-

• The volume of a cuboidal block of silver is 10368 cm². The ratio is 3:2:1.

✯ To Find :-

1. Dimension of the block.
2. Cost of gold polishing its entire surface at Rs 0.50 per cm².

✯ Solution :-

❖ (1) Let, the length, breadth, and height of the cuboidal be 3x, 2x and x

Then, Volume of Cuboid = l × b × h

⇒ $\tt{10368 = 3x × 2x × x}$

⇒ $\tt{10368 = 6x³}$

⇒ $\tt{x³ = \dfrac{10368}{6}}$

⇒ $\tt{x³ = 1728}$

⇒ $\tt{x = \sqrt[3]{1728}}$

➠ x = 12

$\therefore$ Three dimension of the block are,

• Length = 3x = 3(12) = 36
• Breadth = 2x = 2(12) = 24
• Height = x = 12

_________________________________

❖ (2) Total surface area of cuboidal block = 2(lb+bh+hl)

➣ According to the formula,

⇒ $\tt{2(36×24 + 24×12 + 12×36)}$

⇒ $\tt{2(864 + 288 + 432)}$

➩ 3168 cm²

➙ Now, total cost of polishing its entire surface,

⇒ $\tt{3168 × 0.50}$

$\tt\dashrightarrow$ $\sf\boxed{\bold{\large{Rs\: 1584\: cm}}}$

_____________________________