Advertisements
Advertisements
प्रश्न
The sum of the radius and the height of a cylinder is 37 cm and the total surface area of the cylinder is 1628 cm2. Find the height and the volume of the cylinder.
Advertisements
उत्तर
Let r and h be the radius and height of the solid cylinder respectively.
Given, r + h = 37 cm
The total surface area of the cylinder = 1628 cm2 (Given)
∴ `2pir(r + h) = 1628`cm2
⇒ `2pir xx 37 = 1628` cm2
⇒ `2 xx 22/7 xx r xx 37 = 1628`cm2
⇒ `r = (1628 xx 7)/(2 xx 22 xx 37) = 7` cm
rth = 37 cm ⇒ 7 + h = 37 cm ⇒ h = 30 cm
The volume of the cylinder = `pir^2h`
= `22/7 xx 7 xx 7 xx 30 = 4620` cm3
APPEARS IN
संबंधित प्रश्न
A cubical box has each edge 10 cm and another cuboidal box is 12.5 cm long, 10 cm wide and 8 cm high.
(i) Which box has the greater lateral surface area and by how much?
(ii) Which box has the smaller total surface area and by how much?
Find the height of a cuboid whose base area is 180 cm2 and volume is 900 cm3?
A cuboid is of dimensions 60 cm × 54 cm × 30 cm. How many small cubes with side 6 cm can be placed in the given cuboid?
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.
Three equal cubes are placed adjacently in a row. Find the ratio of total surface area of the new cuboid to that of the sum of the surface areas of the three cubes.
Find the volume of a cuboid whose length = 12 cm, breadth = 8 cm, height = 6 cm.
Find the volume of a cuboid whose length = 15 cm, breadth = 2.5 dm, height = 8 cm.
A cuboidal wooden block contains 36 cm3 wood. If it be 4 cm long and 3 cm wide, find its height.
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?
How many planks each of which is 3 m long, 15 cm broad and 5 cm thick can be prepared from a wooden block 6 m long, 75 cm broad and 45 cm thick?
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 cuboidal box is 5 cm by 5 cm by 4 cm. Find its surface area.
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.
Three cubes of metal whose edges are in the ratio 3 : 4 : 5 are melted down in to a single cube whose diagonal is 12 `sqrt(3)` cm. Find the edges of three cubes.
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 volume of wood required to make a closed box of external dimensions 80 cm, 75 cm, and 60 cm, the thickness of walls of the box being 2 cm throughout.
A tank 30 m long, 24 m wide, and 4.5 m deep is to be made. It is open from the top. Find the cost of iron-sheet required, at the rate of ₹ 65 per m2, to make the tank.
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 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 total surface area of a cuboid is 46m2. If its height is 1m and breadth 3m, find its length and volume.
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 room is 5m long, 2m broad and 4m high. Calculate the number of persons it can accommodate if each person needs 0.16m3 of air.
375 persons can be accommodated in a room whose dimensions are in the ratio of 6 : 4 : 1. Calculate the area of the four walls of the room if the each person consumes 64m3 of air.
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.
The total surface area of a cuboid with dimension 10 cm × 6 cm × 5 cm is
