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
The paint in a certain container is sufficient to paint an area equal to 9.375 m2. How many bricks of dimensions 22.5 cm × 10 cm × 7.5 cm can be painted out of this container?
Daniel is painting the walls and ceiling of a cuboidal hall with length, breadth, and height of 15 m, 10 m, and 7 m, respectively. From each can of paint, 100 m2 of area is painted. How many cans of paint will she need to paint the room?
Find the lateral surface area and total surface area of a cube of edge 10 cm.
A 4 cm edge cube is cut into 1 cm edge cubes. Calculate the total surface area of all the small cubes.
A milk container is 8 cm long and 50 cm wide. What should be its height so that it can hold 4 litres of milk?
What will happen to the volume of a cuboid if its Length is doubled, height is same and breadth is halved?
What will be the height of a cuboid of volume 168 m3, if the area of its base is 28 m2?
A rectangular diesel tanker is 2 m long, 2 m wide and 40 cm deep. How many litres of diesel can it hold?
A swimming pool is 250 m long and 130 m wide. 3250 cubic metres of water is pumped into it. Find the rise in the level of water.
The rainfall on a certain day was 6 cm. How many litres of water fell on 3 hectares of field on that day?
The dimensions of an oil tin are 26 cm × 26 cm × 45 cm. Find the area of the tin sheet required for making 20 such tins. If 1 square metre of the tin sheet costs Rs 10, find the cost of tin sheet used for these 20 tins.
A rectangular water reservoir contains 105 m3 of water. Find the depth of the water in the reservoir if its base measures 12 m by 3.5 m.
A field is 150 m long and 100 m wide. A plot (outside the field) 50 m long and 30 m wide is dug to a depth of 8 m and the earth taken out from the plot is spread evenly in the field. By how much is the level of field raised?
If the areas of the adjacent faces of a rectangular block are in the ratio 2 : 3 : 4 and its volume is 9000 cm3, then the length of the shortest edge is
If each edge of a cube, of volume V, is doubled, then the volume of the new cube is
If A1, A2, and A3 denote the areas of three adjacent faces of a cuboid, then its volume is
Length, breadth and height of a cuboid shape box of medicine is 20 cm, 12 cm and 10 cm respectively. Find the surface area of vertical faces and total surface area of this box.
75 persons can sleep in a room 25 m by 9.6 m. If each person requires 16 m3 of the air; find the height of the room.
Find the volume and the total surface area of a cuboid, whose :
length = 15 cm, breadth = 10 cm and height = 8 cm.
The total surface area of a cube is 216 cm2. Find its volume.
The dimension of a class-room are; length = 15 m, breadth = 12 m and height = 7.5 m. Find, how many children can be accommodated in this class-room; assuming 3.6 m3 of air is needed for each child.
A room 5 m long, 4.5 m wide, and 3.6 m high have one door 1.5 m by 2.4 m and two windows, each 1 m by 0.75 m. Find :
(i) the area of its walls, excluding door and windows ;
(ii) the cost of distempering its walls at the rate of Rs.4.50 per m2.
(iii) the cost of painting its roof at the rate of Rs.9 per m2.
A cube of edge 6 cm and a cuboid with dimensions 4 cm x x cm x 15 cm are equal in volume. Find:
(i) the value of x.
(ii) the total surface area of the cuboid.
(iii) the total surface area of the cube.
(iv) which of these two has a greater surface and by how much?
Find the height of the cylinder whose radius is 7 cm and the total surface area is 1100 cm2.
The floor of a rectangular hall has a perimeter 250 m. If the cost of painting the four walls at the rate of ₹ 10 per m2 is ₹ 15,000, find the height of the hall.
A matchbox is 4 cm long, 2.5 cm broad, and 1.5 cm in height. Its outer sides are to be covered exactly with craft paper. How much paper will be required to do so?
Find the Total Surface Area and the Lateral Surface Area of a cuboid whose dimensions are: length = 20 cm, breadth = 15 cm, height = 8 cm
