Question

1. The circumference of the base of a cylindrical vessel is 132 cm and its height is 25 cm.
How many litres of water can it hold? (1000 cm= 11)


2. The inner diameter of a cylindrical wooden pipe is 24 cm and its outer diameter is
28 cm. The length of the pipe is 35 cm. Find the mass of the pipe, if 1 cm' of wood has
a mass of 0.6 g.


3. A soft drink is available in two packs - (i) a tín can with a rectangular base of length
5 cm and width 4 cm, having a height of 15 cm and (ii) a plastic cylinder with circular
base of diameter 7 cm and height 10 cm. Which container has greater capacity and by
how much ?


4. If the lateral surface of a cylinder is 94.2 cm² and its height is 5 cm, then find
(i) radius of its base (ii) its volume. (Use t = 3.14)​

Answer 1

Step-by-step explanation:

1.

Circumference of base = 132cm

$2\pi \: r \: = 132$

$r = 132 \times \frac{7}{22}$

$r = 42 \: cm$

now Volume of Cylinder =

$\pi \: r {}^{2} h$

$= \frac{22}{7} \times 42 \times 42 \times 25$

$= 138600 \: cm {}^{3}$

$= 138.6l$

2.

Inner diameter=24cm

inner radius =12cm

outer diameter =28cm

outer radius=14cm

let outer radius be R and inner radius be r

so mass of pipe =Outer volume - inner volume

volume of cylinder =

$\pi r {}^{2} h$

Mass of pipe is equal to =

$\frac{22}{7} \times 14 \times 14 \times 35 - \frac{22}{7} \times 12 \times 12 \times 35$

$5760 \: cm {}^{3}$

$3456 \: g$

$3.456 \: kg$

mass of pipe =

$5760 \times 0.6$

3.

Volume of tin can with rectangular base

$= l \times b \times h \\ 5 \times 4 \times 15 \\ 300cm {}^{3}$

Diameter of tin with cylindrical base =7cm

radius of tin with cylindrical base=3.5cm

volume of tin =

$\pi \: r {}^{2} \times h \\ \frac{22}{7} \times 3.5 \times 3.5 \times 10 \\ 385 \: cm {}^{3}$

Therefore the thin with cylindrical base has more capacity by 85 cm cube

4.

Lateral surface area of cylinder

$94.2 \: cm { }^{2}$

$2\pi \: r \: h \: = 94.2 \\ 2 \times 3.14 \times 5 = 94.2 \\ r = 94.2 \times \frac{1}{3.14} \times \frac{1}{5} \times \frac{1}{2 } \\ r = 3cm$

Volume of cylinder

$\pi \: r {}^{2} h \\ 3.14 \times 3 \times 3 \times 5 \\ 141.3cm {}^{3}$

I wish it would help you!!!