A metal cube of edge 12 cm is melted and formed into three smaller cubes. If the edges of two smaller cubes are 6 cm and 8 cm, find the edge of third smaller cube.
Mensuration
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A metal cube of edge 12 cm is melted and formed into three smaller cubes. If the edges of two smaller cubes are 6 cm and 8 cm, find the edge of third smaller cube.

KnowledgeBoat · Accepted Answer

Given, Edge of largest cube = 12 cm Edge of 1st smaller cube = 6 cm Edge of 2nd smaller cube = 8 cm. Let the edge of 3rd smaller cube = x cm Calculating the volume of larger cube, Volume = a3 = (12)3 = 1728 cm3. Calculating the volume of smaller cubes, Volume of 1st smaller cube = 63 = 216 cm3. Volume of 2nd smaller cube = 83 = 512 cm3. Volume of 3rd smaller cube = x3. Since larger cube melts to form a smaller cubes, ∴ Volume of larger cube = Total volume of smaller cubes. ⇒ 1728 = 216 + 512 + x3 ⇒ 1728 = 728 + x3 ⇒ x3 = 1728 - 728 ⇒ x3 = 1000 ⇒ x = ⇒ x = 10 cm. Hence, edge of third smaller cube = 10 cm.

Mathematics

A metal cube of edge 12 cm is melted and formed into three smaller cubes. If the edges of two smaller cubes are 6 cm and 8 cm, find the edge of third smaller cube.

Mensuration

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Mathematics

A metal cube of edge 12 cm is melted and formed into three smaller cubes. If the edges of two smaller cubes are 6 cm and 8 cm, find the edge of third smaller cube.

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.

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(ii) the surface area of the cube.

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