Question

The external length, breadth and height of a closed rectangular wooden box are 18 cm, 10 cm and 6 cm respectively and thickness of wood is 1/2 cm. When the box is empty, it weights 15 kg and when filled with sand it weighs 100 kg. Find the weight of the cubic cm of wood and cubic cm of sand.​

Answer 1

Step-by-step explanation:

Given:-

The external length, breadth and height of a closed rectangular wooden box are 18 cm, 10 cm and 6 cm respectively and thickness of wood is 1/2 cm. When the box is empty, it weights 15 kg and when filled with sand it weighs 100 kg

To Find:-

The weight of the cubic cm of wood and cubic cm of sand.

Solution:-

$\rm \: Thickness \: of \: wood = \frac{1}{2} \: cm \\ \rm \: Internal \: length \: of \: wooden \: box = 18 - \bigg( \frac{1}{2} + \frac{1}{2} \bigg) = 18 - 1 = 17 \: cm \\ \\ \rm \: Internal \: breadth \: of \: wooden \: box = 10 - \bigg( \frac{1}{2} + \frac{1}{2} \bigg) = 9 \: cm \\ \\ \rm \: Internal \: depth \: of \: wooden \: box = 6 - \bigg( \frac{1}{2} + \frac{1}{2} \bigg) = 5 \: cm \\ \\ \therefore \: \rm Internal \: volume \: of \: wooden \: box \\ \leadsto \rm \: length \times breadth \times height \\ \leadsto \rm \: (17 \times 9 \times 5) \: {cm}^{3} \\ \\ \rm \: External \: volume \: of \: wood \\ \leadsto \rm \: length \times breadth \times height \\ \leadsto \rm \: (18 \times 10 \times 6) \: {cm}^{3} \\ \rm \leadsto \: 1080 \: {cm}^{3} \\ \\ \rm \: Volume \: of \: wood \: = \: External \: volume - Internal \: volume \\ \rm \longrightarrow \: (1080 - 765) \: {cm}^{3} = 315 \: {cm}^{3} \\ \\ \rm \: \: Weight \: of \: empty \: box = 15 \: kg \\ \implies \: \rm \: Weight \: of \: 315 \: {cm}^{3} wood \: is \: 15 \: kg \\ \therefore \: \rm Weight \: of \: 1 \: {cm}^{3} \: of \: wood = \bigg(\frac{15}{315} \bigg) \: kg = \frac{1}{21} \: kg \\ \tt \: Now \\ \rm \: Volume \: of \: sand = Internal \: volume \: of \: box = 765 \: {cm}^{3} \\ \rm Weight \: of \: sand = Weight \: of \: box \: filled \: with \: sand - Weight \: of \: empty \: box \\ \dashrightarrow \rm \: (100 - 15) \: kg = 85 \: kg \\ \\ \rm Volume \: of \: sand = 765 \: {cm}^{3} \\ \bigstar \red{ \boxed{ \purple{ \rm \: Weight \: of \: 1 \: {cm}^{3} \: of \: sand = \bigg(\frac{85}{725} \bigg) \: kg= \bold{ \frac{1}{9}</u><u>kg</u><u> </u><u>}}}}$

M O R E T O K N O W :

Volume of cube = Length × Breadth × Height

Surface area of cube = 6a²

Surface area of cuboid = 2(lb+bh+lh)

Area of 4 walls of a room = 2(l+b)×h

Answer 2

Solution -

• The external length, breadth and height of a closed rectangular wooden box are 18 cm, 10 cm snd 6 cm respectively.

• The thickness of the wood is ½ cm.

• When it's empty it weighs 15 kg and when filled with sand it weighs 100 kg.

We have to find the weight of sand and wood in cm ³ .

As the box is closed , Internal Sidelength + ½×2 = External Sidelength.

> Internal Length = 18 - 1 = 17 cm

> Internal Breadth = 10-1 = 9 cm

> Internal height = 6-1 = 5 cm

Internal volume = 17 × 9 × 5 cm³ = 315 cm³

External volume = 18 × 10 × 6 cm³ = 1080 cm ³ .

Hence volume of sand is 1080 - 315 = 765 cm³ .

Weight of sand = 100 kg - 15kg = 85 kg.

Weight of wood = 15 kg

Answer : The volume of sand is 765 cm³ and it's weight is 85 kg. The volume of wood is 315 cm ³ and it's weight is 15 kg.

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