Question

An 8 cm thick solid is in the form of a cuboid.If its length and breadth are in the ratio of 3:2 and its volume is 432 cubic cm,find the dimensions of the cuboid.​

Answer 1

Answer:

Length of the cuboid is 9 cm and the breadth of the cuboid is 6 cm.

Step-by-step explanation:

Given :-

• A 8 cm thick solid is in the form of a cuboid.
• Its length and breadth are in the ratio of 3:2.
• Its volume is 432 cm³.

To find :-

• Dimensions of the cuboid.

Solution :-

Let the length of the cuboid be 3x cm and the breadth of the cuboid be 2x cm.

• Height of the cuboid = 8 cm

Formula used :

${\boxed{\sf{Volume\:of\: cuboid=length\times\: breadth\times\: height}}}$

★ Volume of the cuboid is 432 cm³.

According to the question,

length×breadth × height = 432

→ 3x × 2x × 8 = 432

→ 6x² × 8 = 432

→ 6x² = 432/8

→ 6x² = 54

→ x² = 54/6

→ x² = 9

→ x = 3

Therefore,

• Length of the cuboid = 3×3 = 9 cm.
• Breadth of the cuboid = 2×3 = 6 cm.

Answer 2

Answer:

✡ Question ✡

➡ An 8 cm thick solid is in the form of a cuboid.If its length and breadth are in the ratio of 3:2 and its volume is 432 cubic cm,find the dimensions of the cuboid.

✡ Given ✡

➡ An 8 cm thick solid is in the form of a cuboid.

➡ Its length and breadth are in the ratio of 3:2 .

➡ Its volume is 432 cubic cm.

✡ To Find ✡

➡ The dimensions of the cuboid.

✡ Formula Used ✡

$\text{\large\underline{\pink{Volume\: of\: Cuboid\: =\: length\: ×\: breadth\: ×\:height\:}}}$

✡ Solution ✡

➡ Volume of the cuboid is 432 cm³.

▶ According to the question:-

Then,

✴ length × breadth × height = 432

=> 3x × 2x × 8 = 432

=> 6x² × 8 = 432

=> 6x² = 432/8

=> 6x² = 54

=> x² = $\dfrac{54}{8}$

=> x² = 9

=> x = $\bold{\large{\fbox{\color{blue} {3}}}}$

☞ Length of the cuboid = 3×3 = 9 cm.

☞ Breadth of the cuboid = 2×3 = 6 cm.

Step-by-step explanation:

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