Advertisements
Advertisements
Question
The height of a rectangular solid is 5 times its width and its length is 8 times its height. If the volume of the wall is 102.4 cm3, find its length.
Advertisements
Solution
Height of rectangular solid = 5 × width
and length = 8 × height = 8 × 5 × width = 40 × width
Volume = 102.4 cm3
Let width = w
Then height = 40w
and height = 5w
`therefore "w" xx 40"w" xx 5"w" = 102.4`
`"w"^3 = 102.4/(40 xx 5) = 0.512`
= `(0.8)^3`
∴ w = 0.8
∴ Length = 40w = `40 xx 0.8`
= 32 cm
APPEARS IN
RELATED QUESTIONS
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 per m2.
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?
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.
Find the ratio of the total surface area and lateral surface area of a cube.
The length and breadth of a hall are in the ratio 4: 3 and its height is 5.5 metres. The cost of decorating its walls (including doors and windows) at Rs. 6.60 per square metre is Rs. 5082. Find the length and breadth of the room.
A tea-packet measures 10 cm × 6 cm × 4 cm. How many such tea-packets can be placed in a cardboard box of dimensions 50 cm × 30 cm × 0.2 m?
How many soap cakes can be placed in a box of size 56 cm × 0.4 m × 0.25 m, if the size of a soap cake is 7 cm × 5 cm × 2.5 cm?
What will be the height of a cuboid of volume 168 m3, if the area of its base is 28 m2?
How many bricks each of size 25 cm × 10 cm × 8 cm will be required to build a wall 5 m long, 3 m high and 16 cm thick, assuming that the volume of sand and cement used in the construction is negligible?
A solid rectangular piece of iron measures 6 m by 6 cm by 2 cm. Find the weight of this piece, if 1 cm3 of iron weighs 8 gm.
Find the area of the cardboard required to make a closed box of length 25 cm, 0.5 m and height 15 cm.
Show that the product of the areas of the floor and two adjacent walls of a cuboid is the square of its volume.
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.
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?
If the length of a diagonal of a cube is `8 sqrt(3)` cm, then its surface area is
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
The length of the longest rod that can be fitted in a cubical vessel of edge 10 cm long, is
10 cubic metres clay is uniformly spread on a land of area 10 ares. the rise in the level of the ground is
If each edge of a cube is increased by 50%, the percentage increase in its surface area is
The dimensions of a Cinema Hall are 100 m, 60 m, and 15 m. How many persons can sit in the hall if each requires 150 m3 of air?
75 persons can sleep in a room 25 m by 9.6 m. If each person requires 16 m3 of the air; find the height of the room.
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?
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.
A cuboid is 8 m long, 12 m broad and 3.5 high, Find its
(i) total surface area
(ii) lateral surface area
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 matchbox is 4 cm long, 2.5 cm broad, and 1.5 cm in height. Its outer sides are to be covered exactly with craft paper. How much paper will be required to do so?
The total surface area of a cuboid is 46m2. If its height is 1m and breadth 3m, find its length and volume.
A closed box is made of wood 5 mm thick. The external length, breadth and height of the box are 21 cm, 13 cm and 11 cm respectively. Find the volume of the wood used in making the box.
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.
