The square on the diagonal of a cube has an area of 192 cm2. Calculate : (i) the side of the cube. (ii) the total surface area of the cube.

(i) Let a be the side of the cube. The diagonal of the cube forms a square whose area is given: Diagonal of cube = a Since the square has an area of 192 cm2, ⇒ (a )2 = 192 ⇒ a2 x 3 = 192 ⇒ a2 = ⇒ a2 = 64 ⇒ a = ⇒ a ≈ 8 cm Hence, the side of the cube = 8 cm. (ii) The total surface area of cube = 6a2 = 6 x 82 = 6 x 64 = 384 cm2 Hence, the total surface area of the cube = 384 cm2.

The area of cross-section of a pipe is 10.4 cm² and water is running through it at the rate of 54 km/h. If the pipe is always 60% full, find the volume of water, in litres, that flows through the pipe in 5 minutes.

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The volume of a cubical solid is 10368 cm³. If its dimensions are in the ratio 3 : 2 : 1, find the cost of polishing its total surface at the rate of ₹ 2.50 per m².

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Squares, each of side 6 cm are cut off from the four corners of a sheet of tin measuring 42 cm by 30 cm. The remaining portion of the tin sheet is made into an open box by folding up the flaps. Find the capacity of the box formed.

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Mathematics

The square on the diagonal of a cube has an area of 192 cm². Calculate :
(i) the side of the cube.
(ii) the total surface area of the cube.

Mensuration

Related Questions

The area of cross-section of a pipe is 10.4 cm² and water is running through it at the rate of 54 km/h. If the pipe is always 60% full, find the volume of water, in litres, that flows through the pipe in 5 minutes.

The volume of a cubical solid is 10368 cm³. If its dimensions are in the ratio 3 : 2 : 1, find the cost of polishing its total surface at the rate of ₹ 2.50 per m².

Squares, each of side 6 cm are cut off from the four corners of a sheet of tin measuring 42 cm by 30 cm. The remaining portion of the tin sheet is made into an open box by folding up the flaps. Find the capacity of the box formed.

Mathematics

The square on the diagonal of a cube has an area of 192 cm2. Calculate :(i) the side of the cube.(ii) the total surface area of the cube.

Mensuration

Related Questions

The area of cross-section of a pipe is 10.4 cm2 and water is running through it at the rate of 54 km/h. If the pipe is always 60% full, find the volume of water, in litres, that flows through the pipe in 5 minutes.

The volume of a cubical solid is 10368 cm3. If its dimensions are in the ratio 3 : 2 : 1, find the cost of polishing its total surface at the rate of ₹ 2.50 per m2.

Squares, each of side 6 cm are cut off from the four corners of a sheet of tin measuring 42 cm by 30 cm. The remaining portion of the tin sheet is made into an open box by folding up the flaps. Find the capacity of the box formed.

The square on the diagonal of a cube has an area of 192 cm². Calculate :
(i) the side of the cube.
(ii) the total surface area of the cube.

The area of cross-section of a pipe is 10.4 cm² and water is running through it at the rate of 54 km/h. If the pipe is always 60% full, find the volume of water, in litres, that flows through the pipe in 5 minutes.

The volume of a cubical solid is 10368 cm³. If its dimensions are in the ratio 3 : 2 : 1, find the cost of polishing its total surface at the rate of ₹ 2.50 per m².