Advertisements
Advertisements
प्रश्न
The total surface area of a cube is 216 cm2. Find its volume.
Advertisements
उत्तर
6(Edge)2 = Total surface area of a cube
6(Edge)2 = 216 cm2
=> (Edge)2 = `216/6`
=> (Edge)2 = 36
=> Edge = `sqrt(36)`
=> Edge = 6 cm
Volume of the given cube = (Edge)3 = (6)3 = 6 x 6 x 6 = 216 cm3
APPEARS IN
संबंधित प्रश्न
A cubical box has each edge 10 cm and another cuboidal box is 12.5 cm long, 10 cm wide and 8 cm high.
(i) Which box has the greater lateral surface area and by how much?
(ii) Which box has the smaller total surface area and by how much?
Parveen wanted to make a temporary shelter for her car, by making a box-like structure with tarpaulin that covers all the four sides and the top of the car (with the front face as a flap which can be rolled up). Assuming that the stitching margins are very small, and therefore negligible, how much tarpaulin would be required to make the shelter of height 2.5 m, with base dimensions 4 m × 3 m?
Find the height of a cuboid whose base area is 180 cm2 and volume is 900 cm3?
A cuboid is of dimensions 60 cm × 54 cm × 30 cm. How many small cubes with side 6 cm can be placed in the given cuboid?
The length of a hall is 18 m and the width 12 m. The sum of the areas of the floor and the
flat roof is equal to the sum of the areas of the four walls. Find the height of the hall.
The dimensions of a room are 12.5 m by 9 m by 7 m. There are 2 doors and 4 windows in the room; each door measures 2.5 m by 1 .2 m and each window 1 .5 m by I m. Find the cost of painting the walls at Rs. 3.50 per square metre.
Find the volume of a cuboid whose length = 15 cm, breadth = 2.5 dm, height = 8 cm.
Find the height of a cuboid of volume 100 cm3, whose length and breadth are 5 cm and 4 cm respectively.
What will happen to the volume of a cuboid if its Length is doubled, height is same and breadth is halved?
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?
What will be the height of a cuboid of volume 168 m3, if the area of its base is 28 m2?
Find the surface area of a cuboid whose llength = 2 m, breadth = 4 m, height = 5 m .
The walls and ceiling of a room are to be plastered. The length, breadth and height of the room are 4.5 m, 3 m and 350 cm, respectively. Find the cost of plastering at the rate of Rs 8 per square metre.
Find the length of the longest rod that can be placed in a room 12 m long, 9 m broad and 8 m high.
If the volumes of two cubes are in the ratio 8: 1, then the ratio of their edges is
If the sum of all the edges of a cube is 36 cm, then the volume (in cm3) of that cube is
The external dimensions of a closed wooden box are 27 cm, 19 cm, and 11 cm. If the thickness of the wood in the box is 1.5 cm; find:
- The volume of the wood in the box;
- The cost of the box, if wood costs Rs. 1.20 per cm3;
- A number of 4 cm cubes that could be placed into the box.
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 closed box measures 66 cm, 36 cm and 21 cm from outside. If its walls are made of metal-sheet, 0.5 cm thick; find :
(i) the capacity of the box ;
(ii) the volume of metal-sheet and
(iii) weight of the box, if 1 cm3 of metal weighs 3.6 gm.
A tank 30 m long, 24 m wide, and 4.5 m deep is to be made. It is open from the top. Find the cost of iron-sheet required, at the rate of ₹ 65 per m2, to make the tank.
The sum of the radius and the height of a cylinder is 37 cm and the total surface area of the cylinder is 1628 cm2. Find the height and the volume of the cylinder.
If radii of two cylinders are in the ratio 4 : 3 and their heights are in the ratio 5: 6, find the ratio of their curved surfaces.
A cuboid is 8 m long, 12 m broad and 3.5 high, Find its
(i) total surface area
(ii) lateral surface area
In a building, there are 24 cylindrical pillars. For each pillar, the radius is 28 m, and the height is 4 m. Find the total cost of painting the curved surface area of the pillars at the rate of ₹ 8 per m2.
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.
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 Total Surface Area and the Lateral Surface Area of a cuboid whose dimensions are: length = 20 cm, breadth = 15 cm, height = 8 cm
A cuboidal tin box opened at the top has dimensions 20 cm × 16 cm × 14 cm. What is the total area of metal sheet required to make 10 such boxes?
Find the capacity of water tank, in litres, whose dimensions are 4.2 m, 3 m and 1.8 m?
