Advertisements
Advertisements
प्रश्न
Find the length of each edge of a cube, if its volume is :
(i) 216 cm3
(ii) 1.728 m3
Advertisements
उत्तर
(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
संबंधित प्रश्न
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 ratio of the total surface area and lateral surface area of a cube.
Each edge of a cube is increased by 50%. Find the percentage increase in the surface area of the cube.
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.
An open box is made of wood 3 cm thick. Its external length, breadth and height are 1.48 m, 1.16 m and 8.3 m. Find the cost of painting the inner surface of Rs 50 per sq. metre.
Find the volume of a cuboid whose length =1.2 m, breadth = 30 cm, height = 15 cm.
Find the number of cuboidal boxes measuring 2 cm by 3 cm by 10 cm which can be stored in a carton whose dimensions are 40 cm, 36 cm and 24 cm.
The weight of a metal block of size 5 cm by 4 cm by 3 cm is 1 kg. Find the weight of a block of the same metal of size 15 cm by 8 cm by 3 cm.
Find the volume in cubic metre (cu. m) of the cuboid whose dimensions islength = 4 m, breadth = 2.5 m, height = 50 cm.
If V is the volume of a cuboid of dimensions a, b, c and S is its surface area, then prove that \[\frac{1}{V} = \frac{2}{S}\left( \frac{1}{a} + \frac{1}{b} + \frac{1}{c} \right)\]
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 tank open at the top is made of iron sheet 4 m wide. If the dimensions of the tank are 12 m × 8 m × 6 m, find the cost of iron sheet at Rs 17.50 per metre.
If two cubes each of side 6 cm are joined face to face, then find the volume of the resulting cuboid.
The number of cubes of side 3 cm that can be cut from a cuboid of dimensions 10 cm × 9 cm × 6 cm, is ______.
If A1, A2, and A3 denote the areas of three adjacent faces of a cuboid, then its volume is
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.
The volume of a cuboid is 3456 cm3. If its length = 24 cm and breadth = 18 cm ; find its height.
The length, breadth, and height of a cuboid are in the ratio 6: 5 : 3. If its total surface area is 504 cm2; find its dimensions. Also, find the volume of the cuboid.
A closed box is cuboid in shape with length = 40 cm, breadth = 30 cm and height = 50 cm. It is made of a thin metal sheet. Find the cost of metal sheet required to make 20 such boxes, if 1 m2 of metal sheet costs Rs. 45.
How many persons can be accommodated in a big-hall of dimensions 40 m, 25 m, and 15 m; assuming that each person requires 5 m3 of air?
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.
A cuboid is 8 m long, 12 m broad and 3.5 high, Find its
(i) total surface area
(ii) lateral surface area
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.
An open box of length 1.5 m, breadth 1 m, and height 1 m is to be made for use on a trolley for carrying garden waste. How much sheet metal will be required to make this box? The inside and outside surface of the box is to be painted with rust-proof paint. At a rate of 150 rupees per sqm, how much will it cost to paint the box?
Find the volume of wood used in making a closed box 22 cm by 18 cm by 14 cm, using a 1 cm thick wood. Also, find the cost of wood required to make the box at the rate of Rs. 5 per cm³ How many cubes of side 2 cm can be placed in the box?
External dimensions of a closed wooden box are in the ratio 5:4:3. If the cost of painting its outer surface at the rate of Rs 5 per dm2 is Rs 11,750, find the dimensions of the box.
