Advertisements
Advertisements
Question
The height of a circular cylinder is 20 cm and the diameter of its base is 14 cm. Find:
(i) the volume
(ii) the total surface area.
Advertisements
Solution
Height of cylinder (h) = 20 cm
and diameter of its base (d)= 14 cm
and radius of its base (r)= `14/2` = 7 cm
(i) Volume = πr2h
= `22/7 xx 7 xx 7 xx 20` cm3 = 3080 cm3

(ii) Total surface area = 2πr(h + r)
= `2 xx 22/7 xx 7 (20 + 7)` cm2 = 44 x 27 = 1188 cm2
APPEARS IN
RELATED QUESTIONS
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?
A milk container is 8 cm long and 50 cm wide. What should be its height so that it can hold 4 litres of milk?
A water tank is 3 m long, 2 m broad and 1 m deep. How many litres of water can it hold?
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?
The rainfall on a certain day was 6 cm. How many litres of water fell on 3 hectares of field on that day?
An 8 m long cuboidal beam of wood when sliced produces four thousand 1 cm cubes and there is no wastage of wood in this process. If one edge of the beam is 0.5 m, find the third edge.
Find the surface area of a cuboid whose length = 10 cm, breadth = 12 cm, height = 14 cm.
If V is the volume of a cuboid of dimensions a, b, c and S is its surface area, then prove that \[\frac{1}{V} = \frac{2}{S}\left( \frac{1}{a} + \frac{1}{b} + \frac{1}{c} \right)\]
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
If V is the volume of a cuboid of dimensions x, y, z and A is its surface area, then `A/V`
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.
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?
The length, breadth, and height of a cuboid are in the ratio 5 : 3: 2. If its volume is 240 cm3; find its dimensions. Also, find the total surface area of the cuboid.
A solid cube of edge 14 cm is melted down and recast into smaller and equal cubes each of the edge 2 cm; find the number of smaller cubes obtained.
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.
The dining-hall of a hotel is 75 m long; 60 m broad and 16 m high. It has five – doors 4 m by 3 m each and four windows 3 m by 1.6 m each. Find the cost of :
(i) papering its walls at the rate of Rs.12 per m2;
(ii) carpetting its floor at the rate of Rs.25 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.
Find the capacity of a cylindrical container with an internal diameter of 28 cm and a height of 20 cm.
A cylindrical pillar has a radius of 21 cm and a height of 4 m. Find:
- The curved surface area of the pillar.
- cost of polishing 36 such cylindrical pillars at the rate of ₹12 per m2.
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.
Three equal cubes of sides 5cm each are placed to form a cuboid. Find the volume and the total surface area of the cuboid.
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
The total surface area of a cuboid with dimension 10 cm × 6 cm × 5 cm is
A cuboidal tin box opened at the top has dimensions 20 cm × 16 cm × 14 cm. What is the total area of metal sheet required to make 10 such boxes?
