Advertisements
Advertisements
प्रश्न
Find the volume and total surface area of a cube whose each edge is:
(i) 8 cm
(ii) 2 m 40 cm.
Advertisements
उत्तर १
(i)
Edge of the given cube = 8 cm
Volume of the given cube = (Edge)3 = (8)3 = 8 x 8 x 8 = 512 cm3
Total surface area of a cube = 6(Edge)2 = 6 x (8)2 = 384 cm2
(ii)
Edge of the given cube = 2 m 40 cm = 2.40 m
Volume of a cube = (Edge)3
Volume of the given cube = (2.40)3 = 2.40 x 2.40 x 2.40 = 13.824 m2
Total surface area of the given cube = 6 x 2.4 x 2.4 = 34.56 m2
उत्तर २
Formulae for a Cube:
Volume (V): V = a3
Total Surface Area (TSA): TSA = 6a2
(i) Edge length = 8 cm
Volume: V = a3 = 83 = 512 cm3
Total Surface Area: TSA = 6a2 = 6 × 82 = 6 × 64 = 384 cm2
(ii) Edge length = 2 m 40 cm
Convert 2 m 40 cm to centimeters:
2 m = 200 cm, so, 2 m 40 cm = 200 + 40 = 240 cm.
Volume: V = a3 = 2403 = 240 × 240 × 240 = 13,824,000 cm3
Convert to cubic meters:
1 m3 = 1,000,000 cm3 `=>V = (1,38,24,000)/(10,00,000) = 13.224 m^3`
Total Surface Area:
TSA = 6a2 = 6 × 2402 = 6 × 57,600 = 345,600 cm2
Convert to square meters:
`1 m^2 = 10000 cm^2 => TSA = 345600/10000 = 34.56 m^2`
APPEARS IN
संबंधित प्रश्न
A plastic box 1.5 m long, 1.25 m wide and 65 cm deep, is to be made. It is to be open at the top. Ignoring the thickness of the plastic sheet, determine:
(i) The area of the sheet required for making the box.
(ii) The cost of sheet for it, if a sheet measuring 1 m2 costs Rs 20.
A 4 cm edge cube is cut into 1 cm edge cubes. Calculate the total surface area of all the small cubes.
The dimensions of a rectangular box are in the ratio of 2 : 3 : 4 and the difference between the cost ofcovering it with sheet of paper at the rates of Rs. 8 and Rs. 9.50 per m2 is Rs.1248. Find the dimensions of the box.
Ravish wanted to make a temporary shelter for his 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 × 3m?
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.
An ice-cream brick measures 20 cm by 10 cm by 7 cm. How many such bricks can be stored in deep fridge whose inner dimensions are 100 cm by 50 cm by 42 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.
A water tank is 3 m long, 2 m broad and 1 m deep. How many litres of water can it hold?
A rectangular field is 70 m long and 60 m broad. A well of dimensions 14 m × 8 m × 6 m is dug outside the field and the earth dug-out from this well is spread evenly on the field. How much will the earth level rise?
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 dimensions of a cinema hall are 100 m, 50 m and 18 m. How many persons can sit in the hall, if each person requires 150 m3 of air?
The dimensions of a rectangular box are in the ratio of 2 : 3 : 4 and the difference between the cost of covering it with sheet of paper at the rates of Rs 8 and Rs 9.50 per m2 is Rs. 1248. Find the dimensions of the box.
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 the sum of all the edges of a cube is 36 cm, then the volume (in cm3) of that cube is
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.
Find the length of each edge of a cube, if its volume is :
(i) 216 cm3
(ii) 1.728 m3
The total surface area of a cube is 216 cm2. Find its volume.
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.
Find the curved surface area and the total surface area of a right circular cylinder whose height is 15 cm and the diameter of the cross-section is 14 cm.
The length and breadth of a cuboid are 20 cm and 15 cm respectively. If its volume is 2400 cm3, find its height.
A room is 22m long, 15m broad and 6m high. Find the area of its four walls and the cost of painting including doors and windows at the rate of Rs.12per m2.
Three equal cubes of sides 5cm each are placed to form a cuboid. Find the volume and the total surface area of the cuboid.
The length of a cold storage is double its breadth. Its height is 3m. The area of its four walls including doors is 108m2. Find its volume.
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
Find the capacity of water tank, in litres, whose dimensions are 4.2 m, 3 m and 1.8 m?
Three cubes each of side 10 cm are joined end to end. Find the surface area of the resultant figure.
