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
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?
There are two cuboidal boxes as shown in the adjoining figure. Which box requires the lesser amount of material to make?
 |
 |
| (a) | (b) |
Water is pouring into a cubiodal reservoir at the rate of 60 litres per minute. If the volume of the reservoir is 108 m3, find the number of hours it will take to fill the reservoir.
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.
The paint in a certain container is sufficient to paint on area equal to 9.375 m2. How manybricks of dimension 22.5 cm × 10 cm × 7.5 cm can be painted out of this container?
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?
A cuboidal block of solid iron has dimensions 50 cm, 45 cm and 34 cm. How many cuboids of size 5 cm by 3 cm by 2 cm can be obtained from this block? Assume cutting causes no wastage.
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 perimeter of a floor of a room is 30 m and its height is 3 m. Find the area of four walls of the room.
A cuboid has total surface area of 50 m2 and lateral surface area is 30 m2. Find the area of its base.
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 each edge of a cuboid of surface area S is doubled, then surface area of the new cuboid is
The sum of the length, breadth and depth of a cuboid is 19 cm and its diagonal is ` 5 sqrt(5)` cm. Its surface area is
If each edge of a cube is increased by 50%, the percentage increase in its surface area is
If V is the volume of a cuboid of dimensions x, y, z and A is its surface area, then `A/V`
Total surface area of a box of cuboid shape is 500 sq. unit. Its breadth and height is 6 unit and 5 unit respectively. What is the length of that box ?
The volume of a cuboid is 7.68 m3. If its length = 3.2 m and height = 1.0 m; find its breadth.
Four cubes, each of edge 9 cm, are joined as shown below :
Write the dimensions of the resulting cuboid obtained. Also, find the total surface area and the volume
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 internal length, breadth, and height of a closed box are 1 m, 80 cm, and 25 cm. respectively. If its sides are made of 2.5 cm thick wood; find :
(i) the capacity of the box
(ii) the volume of wood used to make the box.
The length, breadth, and height of a cuboid (rectangular solid) are 4 : 3: 2.
(i) If its surface area is 2548 cm2, find its volume.
(ii) If its volume is 3000 m3, find its surface area.
Find the height of the cylinder whose radius is 7 cm and the total surface area is 1100 cm2.
Find the capacity of a cylindrical container with an internal diameter of 28 cm and a height of 20 cm.
A cuboid is 8 m long, 12 m broad and 3.5 high, Find its
(i) total surface area
(ii) lateral surface area
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 surface area of a cuboid formed by joining face to face 3 cubes of side x is 3 times the surface area of a cube of side x.
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.
