(a) Six cubes, each with 12 cm edge, are joined end to end. Find the surface area of the resulting cuboid. (b) The diagonal of a cube is cm. Find its surface area and volume. (c) The areas of three adjacent faces of a cuboid are x, y and z. If the volume is V; prove that : V2 = xyz.

Question

KnowledgeBoat · Accepted Answer

(a) Each cube has an edge length of 12 cm. When 6 cubes are joined end to end in a straight line, the resulting cuboid has: Length = 6 x 12 = 72 cm Breadth = 12 cm Height = 12 cm The surface area of a cuboid = 2(lb + bh + hl) = 2(72 x 12 + 12 x 12 + 12 x 72) = 2 x (864 + 144 + 864) = 2 x 1872 = 3744 cm2 Hence, the surface area of the resulting cuboid = 3744 cm2. (b) Let the side length of the cube be a. The formula for the diagonal of a cube is: Diagonal = a ⇒ = a ⇒ a = 16 cm Surface area of the cube = 6 x side2 = 6 x (16)2 = 6 x 256 = 1536 cm2 Volume of the cube = side3 = (16)3 = 4096 cm3 Hence, the surface area of the cube = 1536 cm2 and its volume = 4096 cm3. (c) Given that the areas of three adjacent faces of a cuboid are x, y, and z, we define: ⇒ x = lb, y = bh and z = lh We also know that the volume of a cuboid = l x b x h Squaring both sides: ⇒ V2 = (lbh)2 ⇒ V2 = l2 b2 h2 ⇒ V2 = (lb) (bh) (hl) ⇒ V2 = x y z ⇒ V2 = xyz Hence, proved V2 = xyz.

Mathematics

(a) Six cubes, each with 12 cm edge, are joined end to end. Find the surface area of the resulting cuboid. (b) The diagonal of a cube is cm. Find its surface area and volume. (c) The areas of three adjacent faces of a cuboid are x, y and z. If the volume is V; prove that : V2 = xyz.

Mensuration

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Mathematics

(a) Six cubes, each with 12 cm edge, are joined end to end. Find the surface area of the resulting cuboid. (b) The diagonal of a cube is cm. Find its surface area and volume. (c) The areas of three adjacent faces of a cuboid are x, y and z. If the volume is V; prove that : V2 = xyz.

Mensuration

Related Questions

The base of an isosceles triangle is 24 cm and its area is 60 cm2. Find its perimeter.

The area of a circular ring enclosed between two concentric circles is 286 cm2. Find the radii of the two circles, given that their difference is 7 cm.

Water flows into a tank, 150 metres long and 100 metres broad, through a pipe whose cross-section is 2 dm by 1.5 dm at the speed of 15 km per hour. In what time, will the water be 3 metres deep ?

A cylindrical bucket holds 44.372 litre of water. The water is emptied into a rectangular tank 66 cm long and 28 cm wide. Find the height of the water level in the tank.

The base of an isosceles triangle is 24 cm and its area is 60 cm². Find its perimeter.

The area of a circular ring enclosed between two concentric circles is 286 cm². Find the radii of the two circles, given that their difference is 7 cm.