Advertisements
Advertisements
Question
Find the length of each edge of a cube, if its volume is :
(i) 216 cm3
(ii) 1.728 m3
Advertisements
Solution
(i)
`("Edge")^3` = Volume of a cube
`("Edge")^3` = 216 cm3
⇒ Edge = `(216)^(1/3)`
⇒ Edge = `(3 xx 3 xx 3 xx 2 xx 2 xx 2)^(1/3)`
⇒ Edge = `3 xx 2`
⇒ Edge = 6 cm.
(ii)
`("Edge")^3` = Volume of a cube
`("Edge")^3` = 1.728 m3
⇒ `("Edge")^3 = 1.728/1.000 = 1728/1000`
⇒ Edge = `(1728/1000)^(1/3)`
⇒ Edge = `((2 xx 2xx 2 xx 2 xx 2 xx 2 xx 3 xx 3 xx 3)/(10 xx 10 xx 10))^(1/3)`
⇒ Edge = `(2 xx 2 xx 3)/10`
⇒ Edge = `12/10`m
⇒ Edge = 1.2 m
APPEARS IN
RELATED QUESTIONS
Find the height of a cuboid whose base area is 180 cm2 and volume is 900 cm3?
The length, breadth and height of a room are 5 m, 4 m and 3 m respectively. Find the cost
of white washing the walls of the room and the ceiling at the rate of Rs. 7.50 m2.
Three cuboids of dimensions 5 cm × 6 cm × 7cm, 4cm × 7cm × 8 cm and 2 cm × 3 cm × 13 cm are melted and a cube is made. Find the side of cube.
How many wooden cubical blocks of side 25 cm can be cut from a log of wood of size 3 m by 75 cm by 50 cm, assuming that there is no wastage?
How many soap cakes can be placed in a box of size 56 cm × 0.4 m × 0.25 m, if the size of a soap cake is 7 cm × 5 cm × 2.5 cm?
A tank is 8 m long, 6 m broad and 2 m high. How much water can it contain?
The length , breadth and height of a room are 5 m, 4.5 m and 3 m, respectively. Find the volume of the air it contains.
The rainfall on a certain day was 6 cm. How many litres of water fell on 3 hectares of field on that day?
If V is the volume of a cuboid of dimensions a, b, c and S is its surface area, then prove that \[\frac{1}{V} = \frac{2}{S}\left( \frac{1}{a} + \frac{1}{b} + \frac{1}{c} \right)\]
The breadth of a room is twice its height, one half of its length and the volume of the room is 512 cu. dm. Find its dimensions.
A closed iron tank 12 m long, 9 m wide and 4 m deep is to be made. Determine the cost of iron sheet used at the rate of Rs 5 per metre sheet, sheet being 2 m wide.
The external dimensions of a closed wooden box are 48 cm, 36 cm, 30 cm. The box is made of 1.5 cm thick wood. How many bricks of size 6 cm × 3 cm × 0.75 cm can be put in this box?
If the length of a diagonal of a cube is `8 sqrt(3)` cm, then its surface area is
The area of the floor of a room is 15 m2. If its height is 4 m, then the volume of the air contained in the room is
If V is the volume of a cuboid of dimensions x, y, z and A is its surface area, then `A/V`
Find the volume and the total surface area of a cuboid, whose :
length = 15 cm, breadth = 10 cm and height = 8 cm.
Find the volume and total surface area of a cube whose each edge is:
(i) 8 cm
(ii) 2 m 40 cm.
The length, breadth, and height of a room are 6 m, 5.4 m, and 4 m respectively. Find the area of :
(i) its four-walls
(ii) its roof.
The dining-hall of a hotel is 75 m long; 60 m broad and 16 m high. It has five – doors 4 m by 3 m each and four windows 3 m by 1.6 m each. Find the cost of :
(i) papering its walls at the rate of Rs.12 per m2;
(ii) carpetting its floor at the rate of Rs.25 per m2.
The capacity of a rectangular tank is 5.2 m3 and the area of its base is 2.6 x 104 cm2; find its height (depth).
The curved surface area of a cylinder of height 14 cm is 88 cm2. Find the diameter of the base of the cylinder.
The curved surface area and the volume of a toy, cylindrical in shape, are 132 cm2 and 462 cm3 respectively. Find, its diameter and its length.
The length breadth and height of a cuboid are in the ratio of 3 : 3 : 4. Find its volume in m3 if its diagonal is `5sqrt(34)"cm"`.
A square plate of side 'x' cm is 4 mm thick. If its volume is 1440 cm3; find the value of 'x'.
A closed box is made of wood 5 mm thick. The external length, breadth and height of the box are 21 cm, 13 cm and 11 cm respectively. Find the volume of the wood used in making the box.
Opposite faces of a cuboid are ______ in area.
Find the capacity of water tank, in litres, whose dimensions are 4.2 m, 3 m and 1.8 m?
