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?
Advertisements
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
There are two cuboidal boxes as shown in the adjoining figure. Which box requires the lesser amount of material to make?
 |
 |
| (a) | (b) |
Find the lateral surface area and total surface area of a cube of edge 10 cm.
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 height of a cuboid of volume 100 cm3, whose length and breadth are 5 cm and 4 cm respectively.
A cuboidal block of silver is 9 cm long, 4 cm broad and 3.5 cm in height. From it, beads of volume 1.5 cm3 each are to be made. Find the number of beads that can be made from the block.
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.
Find the volume in cubic metre (cu. m) of the cuboid whose dimensions islength = 4 m, breadth = 2.5 m, height = 50 cm.
Find the surface area of a cuboid whose length = 10 cm, breadth = 12 cm, height = 14 cm.
A cuboidal box is 5 cm by 5 cm by 4 cm. Find its surface area.
The central hall of a school is 80 m long and 8 m high. It has 10 doors each of size 3 m × 1.5 m and 10 windows each of size 1.5 m × 1 m. If the cost of white-washing the walls of the hall at the rate of Rs 1.20 per m2 is Rs 2385.60, fidn the breadth of the hall.
Find the length of the longest rod that can be placed in a room 12 m long, 9 m broad and 8 m high.
Find the edge of a cube whose surface area is 432 m2.
If the volumes of two cubes are in the ratio 8: 1, then the ratio of their edges is
If each edge of a cuboid of surface area S is doubled, then surface area of the new cuboid is
Volume of a cuboid is 12 cm3. The volume (in cm3) of a cuboid whose sides are double of the above cuboid 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
Length, breadth and height of a cuboid shape box of medicine is 20 cm, 12 cm and 10 cm respectively. Find the surface area of vertical faces and total surface area of this box.
Find the length of each edge of a cube, if its volume is :
(i) 216 cm3
(ii) 1.728 m3
A wall 9 m long, 6 m high and 20 cm thick, is to be constructed using bricks of dimensions 30 cm, 15 cm, and 10 cm. How many bricks will be required?
Find the area of metal-sheet required to make an open tank of length = 10 m, breadth = 7.5 m and depth = 3.8 m.
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.
A metallic sheet is of the rectangular shape with dimensions 48cm x 36cm. From each one of its corners, a square of 8cm is cutoff. An open box is made of the remaining sheet. Find the volume of the box.
The areas of any two faces of a cuboid are equal.
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.
