Question

The diameter of a cone is 28 cm and slant height is 10.5 cm. Then, its lateral surface area is :

(A) 480 cm2 (B) 490 cm2 (C) 462 cm2 (D) 466 cm2​

Answer 1

Given :-

• Slant Height = 10.5 cm
• Diameter = 28 cm
• Radius = Diameter ÷ 2 = 28 ÷ 2 = 14 cm

To Find :-

• CSA of cone = ?

Answer :-

• CSA of cone = 462 cm²

Explaination :-

→ CSA of cone = πrl

→ CSA of cone = 22/7 × 14 × 10.5

→ CSA of cone = 22 × 2 × 10.5

→ CSA of cone = 44 × 10.5

→ CSA of cone = 462 cm²

Therefore,Lateral Surface Area of cone is (C) 462 cm².

_____________________

Extra Shots :-

• 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

Answer 2

$\underline{\underline{\underline{\underline{\mathfrak{\blue{ \:\:\:Solution:-\:\:\:}}}}}}$

$\leadsto\bf \dfrac{Diameter}{2} = Radius$

$\leadsto\bf \cancel\dfrac{28}{2} = Radius$

$\leadsto\underline{\boxed{\textsf{ {\textbf{462 cm²}}}}} \qquad\qquad \bigg\lgroup\bold{Radius } \bigg\rgroup$

$\small\underline\textsf{ Formula Used:- }$

${\underline{\overline{\mid{\mathsf{\purple{\:\: Curved \:surface\: area\: of\: circle = \pi rl\:\:} \mid}}}}}$

$\small\underline\textsf{ Putting the values:-}$

$\leadsto\bf Curved\: surface \:area \:of \:circle = \dfrac{22}{7} \times \cancel{14} \times 10.5$

$\leadsto \bf Curved\: surface \:area\: of \:circle = 44 \times 10.5$

$\leadsto\bf Curved \:surface \:area \:of \:circle = 462 cm^2$

$\small\underline\textsf{ Hence:-}$

$\underline{\boxed{\textsf{Lateral surface area = {\textbf{462 cm²}}}}} \qquad\qquad \bigg\lgroup\bold{Option \ C \ is \ Correct } \bigg\rgroup$