Advertisements
Advertisements
प्रश्न
The square on the diagonal of a cube has an area of 441 cm2. Find the length of the side and total surface area of the cube.
उत्तर
Area of a Square = 441cm2
side2 = 441
side = `sqrt(441)`
∴ side = 21cm
∴ The length of the diagonals of the cube is 21cm.
Let 'a' be the side of the cube
Diagonal of a cube = `sqrt(3) xx "a"`
∴ 21 = `sqrt(3) xx "a"`
a = `(21)/sqrt(3)`
a = `(21)/sqrt(3) xx sqrt(3)/sqrt(3)`
(rationalising the denominator)
a = `(21sqrt(3))/(3)`
a = `7sqrt(3)"cm"`
Total surface area of a cube
= 6a2
= 6 x `(7sqrt(3))^2`
= 6 x 49 x 3
= 882cm2
∴ Side of the cube is `7sqrt(3)"cm"` and the total surface area of the cube is 882cm2.
APPEARS IN
संबंधित प्रश्न
If each edge of a cube is doubled, how many times will its volume increase?
Find the volume of a cube whose side is 1.5 dm .
Fill in the blank in the following so as to make the statement true:
1 kl = ....... m3
Fill in the blank in the following so as to make the statement true:
1 ml = ........ cu. cm
Three cubes whose edges measure 3 cm, 4 cm, and 5 cm respectively are melted to form a new cube. Find the surface area of the new cube formed.
Three cubes, whose edges are x cm, 8 cm, and 10 cm respectively, are melted and recast into a single cube of edge 12 cm. Find 'x'.
The volume of a cube is 1331 cm3. Find its total surface area.
A cuboid is 25cm long, 15cm board and 9cm high. Find the whole surface of a cube having its volume equal to that of the cuboid.
The lateral surface area of a cube of side 12 cm is
A river 2 m deep and 45 m wide is flowing at the rate of 3 km per hour. Find the amount of water in cubic metres that runs into the sea per minute.
