Question

Find the curved surface area and the total surface area of a solid cone whose slant height and the vertical height are 58cm and 40cm respectively

Answer 1

Question :

Find the curved surface area and the total surface area of a solid cone whose slant height and the vertical height are 58cm and 40cm respectively.

Answer :

Curved Surface Area = 7,656 cm² .

Total Surface Area = 13,200 cm² .

For full solution refer to the above attachment

Answer 2

$\sf{ \large{ \green{ \underline{QUESTION: }}}}$

$\sf{ \red{ \tiny{Find \: the \: curved \: surface \: area \: and \: the \: total \: surface \: area \: of \: a \: solid \: cone }}} \\ \sf{ \tiny{ \green{ \: whose \: slant \: height \: and \: the \: vertical \: \: height \: are \: 58cm \: and \: 40cm \: respectively ?}}}$

$\sf{ \large{ \blue{ \tt{ \underline{SOLUTION: }}}}}$

▶Given:

↪ Slant Height = 58 Centimeters

↪ Vertical Height = 40 Centimeters

▶To Find = Base of Radius ?

▶ We know that [l²=h²+r²]

Here, L is denotes Slant Height , H denotes Vertical Height and r denotes Base of Radius of Cone.

↪l²=h²+r²

↪ (58)² = (40)² + (r)²

↪ (58)²-(40)²=(r)²

↪ (58+40)(58-40)= r²

↪ (98)(18)=r²

↪ 1764 = r²

↪√1764=r

↪ r = 42 Cm

Now, According to the Question's Statement ↩

↪ Statement : Find the curved surface area and the total surface area of a solid cone ?

↪ Curved Surface of area = πrl

↪ Curved Surface of area =22/7×42×58

↪Curved Surface of area = 22×6×58

↪Curved Surface of area = 7656cm²

▶Hence, Curved Surface of area is (7656cm²)↪

Again, According to the Question's Statement!

↪ Statement : The total surface area of a solid cone ?

Total Surface Area of Cone = πr(l+r)

↪ Total Surface Area of Cone =π(42)[(58+42)

↪Total Surface Area of Cone =π(42)(100)

↪Total Surface Area of Cone =22/7×42×100

↪Total Surface Area of Cone =22×6×100

↪Total Surface Area of Cone =2200×6

↪Total Surface Area of Cone = 13,200cm²