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.
Advertisements
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
Describe how the two figures at the right are alike and how they are different. Which box has larger lateral surface area?
Find the volume of a cube whose side is 8 cm .
What will happen to the volume of a cube, if its edge is halved ?
Find the volume of a cube whose surface area is 96 cm2.
Side of a cube is 4.5 cm. Find the surface area of all vertical faces and total surface area of the cube.
Four identical cubes are joined end to end to form a cuboid. If the total surface area of the resulting cuboid as 648 m2; find the length of the edge of each cube. Also, find the ratio between the surface area of the resulting cuboid and the surface area of a cube.
The ratio between the lengths of the edges of two cubes is in the ratio 3: 2. Find the ratio between their:
(i) total surface area
(ii) volume.
Three metal cubes with edges 6cm, 8cm and 10cm respectively are melted together and formed into a single cube. Find the diagonal of this cube.
A cube of side 5 cm is cut into as many 1 cm cubes as possible. What is the ratio of the surface area of the original cube to that of the sum of the surface areas of the smaller cubes?
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.
