Question

1. The curved surface area of a cone is 4070 cm2 and its diameter is 70 cm. Calculate its :
(i) slant height; (ii) height and (iii) volume.
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Answer 1

Answer:

L = 37 cm, H = 12 cm, V = 15,400 cm³

given: CSA of cone = 4070 cm², d = 70 cm

=> r = d/2 = 70/2 = 35 cm

to find: (1) slant height L

(2) height H

(3) volume V

(1) CSA = πrL

=> 4070 = 22/7*35*L

=> L = (4070*7)/22*35

=> 37 cm

(2) H = √ (L² - r²)

=> H = √(37² - 35²)

=> H = √(144)

=> H = 12 cm

(3) Volume V = 1/3πr²h

V = 1/3*22/7*35²*12

=> V = 15,400 cm³

Answer 2

Answer:

L = 37 cm, H = 12 cm, V = 15,400 cm³

given: CSA of cone = 4070 cm², d = 70 cm

=> r = d/2 = 70/2 = 35 cm

to find: (1) slant height L

(2) height H

(3) volume V

(1) CSA = πrL

=> 4070 = 22/7*35*L

=> L = (4070*7)/22*35

=> 37 cm

(2) H = √ (L² - r²)

=> H = √(37² - 35²)

=> H = √(144)

=> H = 12 cm

(3) Volume V = 1/3πr²h

V = 1/3*22/7*35²*12

=> V = 15,400 cm³