Question

Q20. A right triangle ABC with sides5cin, 12cm, 13crn is revolved about the side 12 cm. Find the Córved Surface Area
and the Volume of the Solid so obtained​

Answer 1

☆Given Question :-

• A right triangle ABC with sides 5 cm, 12cm, 13cm is revolved about the side 12 cm. Find the Curved Surface Area and the Volume of the Solid so obtained.

${ \boxed {\sf{Given}}}$

• A right triangle ABC with sides 5 cm, 12cm, 13cm is revolved about the side 12 cm.

${ \boxed {\sf{To Find}}}$

• Curved Surface Area and the Volume of the Solid so obtained.

${ \boxed {\sf{Formula used :- }}}$

${{ \boxed{\large{\bold\red{Volume_{(Cone)}\: = \dfrac{1}{3} \:\pi r^2 h }}}}}$

${{ \boxed{\large{\bold\green{Curved \: Surface Area_{(Cone)}\: = \:\pi rl}}}}}$

${ \boxed {\bf{Solution}}}$

☆ Let us consider a triangle ️ ABC, right angled at B.

☆ So, AC be the Hypotenuse, AC = 13 cm

☆ AB = 12 cm and BC = 5 cm.

When the triangle is revolved around the side 12cm, the solid obtained is a cone with height 12cm, radius 5cm and slant height 13cm.

So,

$\sf \: ⟼Radius, r = 5 cm$

$\sf \: ⟼Height, h = 12 cm$

$\sf \: ⟼Slant \: height, l = 13 \: cm.$

$\bf \:Curved \: Surface \: Area \: of \: cone = \pi \:rl$

$\sf \:Curved \: Surface \: Area \: of \: cone = \dfrac{22 }{7} \times 5 \times 13$

$⟼\sf \:Curved \: Surface \: Area \: of \: cone = \dfrac{1430}{7} \: {cm}^{2}$

$\bf \:Volume \: of \: cone = \dfrac{1}{3} \pi \: {r}^{2} h$

$⟼\sf \:Volume \: of \: cone = \dfrac{1}{3} \times \dfrac{22}{7} \times {5}^{2} \times 12$

$\sf \: ⟼\sf \:Volume \: of \: cone = \dfrac{2200}{7} \: {cm}^{3}$

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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