Question

A chord of circle of a radius 28 cm subtends a right angle at the centre. What is the area of the minor sector?
(Use The curved surface area of a cylinder of height 14 cm is 88 cm", find the diameter of the cylinder.​)​

Answer 1

Area of minor sector is 616 cm^2.

Step-by-step explanation:

Angle of sector = 90

Radius = 28 cm

Area of minor sector = angle of sector /360 × pie r^2

= 90 / 360 × 22/7 × 28 × 28

= 22 × 28

= 616 cm^2

Answer 2

$\large\underline{\sf{Solution-}}$

Given that,

↝ Radius of circle, r = 28 cm

↝ Sector angle, x = 90°

We know,

$\red{\rm :\longmapsto\:\boxed{ \tt{ \: Area_{(sector)} = \pi \: {r}^{2} \: \frac{x}{360} \: }}}$

Where,

↝ r is radius of sector

↝ x is sector angle or central angle.

So, on substituting the values of x and r, we get

$\rm :\longmapsto\:Area_{(sector)} = \dfrac{22}{7} \times {(28)}^{2} \times \dfrac{90}{360}$

$\rm :\longmapsto\:Area_{(sector)} = \dfrac{22}{7} \times 28 \times 28 \times \dfrac{1}{4}$

$\rm :\longmapsto\:Area_{(sector)} = 22 \times 28$

$\bf\implies \:\boxed{ \tt{ \: Area_{(sector)} = 616 \: {cm}^{2} \: }}$

$\red{\large\underline{\sf{Solution-2}}}$

Given that,

↝ Curved Surface Area of cylinder = 88 sq. cm

↝ Height of cylinder, h = 14 cm

Let assume that radius of cylinder be 'r' cm.

We know,

$\red{\rm :\longmapsto\:\boxed{ \tt{ \: CSA_{(cylinder)} = 2 \: \pi \: r \: h \: }}}$

Where,

↝ CSA is Curved Surface Area

↝ h is height of cylinder

↝ r is radius of cylinder

So, on substituting the values, we get

$\rm :\longmapsto\:88 = 2 \times \dfrac{22}{7} \times r \times 14$

$\rm :\longmapsto\:88 = (2r) \times 22 \times 2$

$\rm :\longmapsto\:88 = 44 \times diameter$

$\red{\bigg \{ \because \:diameter \: = \: 2 \: r \bigg \}}$

$\rm \implies\:\boxed{ \tt{ \: diameter \: = \: 2 \: cm \: }}$

More information :-

Perimeter of rectangle = 2(length× breadth)

Diagonal of rectangle = √(length ²+breadth ²)

Area of square = side²

Perimeter of square = 4× side

Volume of cylinder = πr²h

T.S.A of cylinder = 2πrh + 2πr²

Volume of cone = ⅓ πr²h

C.S.A of cone = πrl

T.S.A of cone = πrl + πr²

Volume of cuboid = l × b × h

C.S.A of cuboid = 2(l + b)h

T.S.A of cuboid = 2(lb + bh + lh)

C.S.A of cube = 4a²

T.S.A of cube = 6a²

Volume of cube = a³

Volume of sphere = 4/3πr³

Surface area of sphere = 4πr²

Volume of hemisphere = ⅔ πr³

C.S.A of hemisphere = 2πr²

T.S.A of hemisphere = 3πr²