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
Find the height of a cuboid whose base area is 180 cm2 and volume is 900 cm3?
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.
What will happen to the volume of a cuboid if its Length is doubled, height is doubled and breadth is sama?
The weight of a metal block of size 5 cm by 4 cm by 3 cm is 1 kg. Find the weight of a block of the same metal of size 15 cm by 8 cm by 3 cm.
A rectangular diesel tanker is 2 m long, 2 m wide and 40 cm deep. How many litres of diesel can it hold?
A water tank is 3 m long, 2 m broad and 1 m deep. How many litres of water can it hold?
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 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.
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 surface area of a cuboid whose llength = 2 m, breadth = 4 m, height = 5 m .
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.
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 wall.
If the volumes of two cubes are in the ratio 8: 1, then the ratio of their edges is
A cuboid has total surface area of 372 cm2 and its lateral surface area is 180 cm2, find the area of its base.
The length of the longest rod that can be fitted in a cubical vessel of edge 10 cm long, is
If each edge of a cuboid of surface area S is doubled, then surface area of the new 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
The length, breadth and height of a rectangular solid are in the ratio 5 : 4 : 2. If the total surface area is 1216 cm2, find the length, the breadth and the height of the solid.
A room 5 m long, 4.5 m wide, and 3.6 m high have one door 1.5 m by 2.4 m and two windows, each 1 m by 0.75 m. Find :
(i) the area of its walls, excluding door and windows ;
(ii) the cost of distempering its walls at the rate of Rs.4.50 per m2.
(iii) the cost of painting its roof at the rate of Rs.9 per m2.
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 total surface area of a cylinder is 6512 cm2 and the circumference of its bases is 88 cm. Find:
(i) its radius
(ii) its volume
If radii of two cylinders are in the ratio 4 : 3 and their heights are in the ratio 5: 6, find the ratio of their curved surfaces.
An open box of length 1.5 m, breadth 1 m, and height 1 m is to be made for use on a trolley for carrying garden waste. How much sheet metal will be required to make this box? The inside and outside surface of the box is to be painted with rust-proof paint. At a rate of 150 rupees per sqm, how much will it cost to paint the box?
Find the volume of wood used in making a closed box 22 cm by 18 cm by 14 cm, using a 1 cm thick wood. Also, find the cost of wood required to make the box at the rate of Rs. 5 per cm³ How many cubes of side 2 cm can be placed in the box?
The total surface area of a cuboid with dimension 10 cm × 6 cm × 5 cm is
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.
Three cubes each of side 10 cm are joined end to end. Find the surface area of the resultant figure.
