Question

the radius and height of a right circular cone are in the ratio 4 : 3 and its volume is 2156 cu.cm. find the CSA and TSA of a cone.

Answer 1

let the common factor be x 
So radius and height would be 3x and 4 x respectively. 
Volume of cone is 1/3 pi*r^2*h 
so, 
301.44=1/3 pi*36x^3 
find appropriate value for x and then for slant height use pythagoras formula. 
after finding x,multiply x by 3 to get radius and by 4 to get height. 
Now by pythagoras theorem, 
r^2 +h^2 =l^2 

Answer 2

Answer:

Curved surface area of cone = 770 cm²

Total Surface area of cone = 1386 cm²

Step-by-step explanation:

Volume of a cone = (1/3)π r² h

r = Radius

h = Height

Let say radius = 4x cm

then height = 3x  cm

Volume of a cone = (1/3) (22/7) (4x)² (3x)

= (22/7) (16) x³

(22/7) (16) x³ = 2156

=> x³ = (2156 * 7) / (22 * 16)

=> x³ = 98 * 7 / 16

=> x³ = 49 * 7 / 8

=> x³ = 7³/2³

=> x = 7/2

Radius = 4x = 4*7/2 = 14cm

Height = 3*7/2 = 10.5 cm

Slant Height = l cm

l² = r² + h²

=> l² = 14² + (10.5)²

=> l² = 196 + 110.25

=> l² = 306.25

=> l = 17.5 cm

Curved Surface Area = π r l

= (22/7) * 14 * 17.5

= 44 * 17.5

= 770 cm²

Curved surface area of cone = 770 cm²

Total Surface Area = π r² + π r l

= (22/7) * 14² + 770

= 616 + 770

= 1386 cm²

Total Surface area of cone  = 1386 cm²

please please mark my answer as brainliest answer.

and also follow me...✔️✔️

thx.... ❤❤❤❤❤