(i) How many cubic cm of iron are there in an open box whose external dimensions are 36 cm, 25 cm and 16.5 cm, the iron being 1.5 cm thick throughout ?
(ii) If 1 cm³ of iron weighs 15 g, find the weight of the empty box in kg.

Question

(i) How many cubic cm of iron are there in an open box whose external dimensions are 36 cm, 25 cm and 16.5 cm, the iron being 1.5 cm thick throughout ?
(ii) If 1 cm³ of iron weighs 15 g, find the weight of the empty box in kg.

KnowledgeBoat · Accepted Answer

(i) Given, External dimensions : Length (L) = 36 cm Breadth (B) = 25 cm Height (H) = 16.5 cm Internal dimensions: Since the thickness = 1.5 cm ∴ Length (l) = 36 - (1.5 + 1.5) = 36 - 3 = 33 cm Breadth (b) = 25 - (1.5 + 1.5) = 25 - 3 = 22 cm Height (h) = 16.5 - 1.5 = 15 cm (Since, box is open) Calculating the external volume, Volume = L × B × H = 36 × 25 × 16.5 = 14,850 cm3. Calculating internal volume, Volume = l × b × h = 33 × 22 × 15 = 10,890 cm3 Calculating volume of iron, Volume of iron = External volume - Internal volume = 14,850 - 10,890 = 3,960 cm3. Hence, volume of iron = 3,960 cm3. (ii) Given, Weight of iron = 15 g Total weight of the box = Volume of iron × weight of iron. = 3,960 × 15 g = 59,400 g. 1000 g = 1 kg ∴ 59,400 g = kg = 59.4 kg Hence, weight of the box = 59.4 kg.

Mathematics

(i) How many cubic cm of iron are there in an open box whose external dimensions are 36 cm, 25 cm and 16.5 cm, the iron being 1.5 cm thick throughout ?
(ii) If 1 cm³ of iron weighs 15 g, find the weight of the empty box in kg.

Mensuration

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Mathematics

(i) How many cubic cm of iron are there in an open box whose external dimensions are 36 cm, 25 cm and 16.5 cm, the iron being 1.5 cm thick throughout ?(ii) If 1 cm3 of iron weighs 15 g, find the weight of the empty box in kg.

Mensuration

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(i) How many cubic cm of iron are there in an open box whose external dimensions are 36 cm, 25 cm and 16.5 cm, the iron being 1.5 cm thick throughout ?
(ii) If 1 cm³ of iron weighs 15 g, find the weight of the empty box in kg.

The surface area of a cube is 1536 cm². Find :
(i) the length of its edge
(ii) its volume
(iii) the volume of its material whose thickness is 5 mm.

Two cubes, each of volume 512 cm³ are joined end to end. Find the surface area of the resulting cuboid.

The dimensions of a metallic cuboid are 100 cm × 80 cm × 64 cm. It is melted and recast into a cube. Find :
(i) the edge of the cube,
(ii) the surface area of the cube.