Advertisements
Advertisements
Question
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?
Solution
Edge of a cube = 6 cm
Volume = a3 = (6)3 = 216 cm3
Dimensions of a cuboid = 4 cm x x cm x 15 cm
Volume = 60x cm3
The volume of both is equal
(i) ∴ `60x = 216 ⇒ x = 216/60 = 36/10`
∴ x = 3.6 cm
(ii) Total surface area of cuboid
= 2[lb + bh + hl]
= `2[4 xx 3.6 + 3.6 xx 15 + 15 xx 4]` cm2
= 2[14.4 + 54.0 + 60] cm2
= `128.4 xx 2 = 256.8` cm2
(iii) Total surface area of cube
= `6a^2 = 6(6)^2 = 6 xx 36 = 216` cm2
(iv) Difference of surface areas = 256.8 - 216
= 40.8 cm2
∴ Surface area of cuboid is greater
APPEARS IN
RELATED QUESTIONS
Shanti Sweets Stall was placing an order for making cardboard boxes for packing their sweets. Two sizes of boxes were required. The bigger of dimensions 25 cm × 20 cm × 5 cm and the smaller of dimensions 15 cm × 12 cm × 5 cm. For all the overlaps, 5% of the total surface area is required extra. If the cost of the cardboard is Rs 4 for 1000 cm2, find the cost of cardboard required for supplying 250 boxes of each kind.
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?
The length, breadth and height of a room are 5 m, 4 m and 3 m respectively. Find the cost
of white washing the walls of the room and the ceiling at the rate of Rs. 7.50 m2.
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?
Find the volume of a cuboid whose length = 12 cm, breadth = 8 cm, height = 6 cm.
Find the volume in cubic metre (cu. m) of the cuboid whose dimensions is length = 10 m, breadth = 25 dm, height = 50 cm.
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?
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.
Find the surface area of a cuboid whose length = 6 dm, breadth = 8 dm, height = 10 dm.
A swimming pool is 20 m long 15 m wide and 3 m deep. Find the cost of repairing the floor and wall at the rate of Rs 25 per square metre.
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 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.
The length, width and height of a rectangular solid are in the ratio of 3 : 2 : 1. If the volume of the box is 48cm3, the total surface area of the box is
Three equal cubes are placed adjacently in a row. The ratio of the total surface area of the resulting cuboid to that of the sum of the surface areas of three cubes, is
On a particular day, the rain fall recorded in a terrace 6 m long and 5 m broad is 15 cm. The quantity of water collected in the terrace is
A cube whose volume is 1/8 cubic centimeter is placed on top of a cube whose volume is 1 cm3. The two cubes are then placed on top of a third cube whose volume is 8 cm3. The height of the stacked cubes is
Find the volume and the total surface area of a cuboid, whose :
length = 15 cm, breadth = 10 cm and height = 8 cm.
Find the volume and the total surface area of a cuboid, whose :
l = 3.5 m, b = 2.6 m and h = 90 cm
The volume of a cuboid is 7.68 m3. If its length = 3.2 m and height = 1.0 m; find its breadth.
Find the volume and total surface area of a cube whose each edge is:
(i) 8 cm
(ii) 2 m 40 cm.
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 external dimensions of an open wooden box are 65 cm, 34 cm, and 25 cm. If the box is made up of wood 2 cm thick, find the capacity of the box and the volume of wood used to make it.
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 length breadth and height of a cuboid are in the ratio of 3 : 3 : 4. Find its volume in m3 if its diagonal is `5sqrt(34)"cm"`.
A square plate of side 'x' cm is 4 mm thick. If its volume is 1440 cm3; find the value of 'x'.
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
Three identical cubes of side 4 cm are joined end to end. Find the total surface area and lateral surface area of the new resulting cuboid
