17.
The curved surface area of a cone is 306 cm' and its slant height is 14 cm, find
(a) radius of the base
(b) total surface area of the cone.
OR
If the lateral surface of a cylinder is 94.2 cm and its height is 5 cm, then find
(a) radius of its base
(b) its volume
life times of 400 near lamps
900-1000
Answers
Answer:
17. (i) (a) 7 cm (approximated from 6.95 cm)
(ii) 462 cm²
(ii) (a) 3 cm
(b) 141.3 cm³
Step-by-step explanation:
This is an OR question, but I am going to answer both so that if one of them (or a similar question) comes up, you can solve it.
(i) (a) CSA of cone = πrl = 306
l = slant height = 14 cm
=> (22/7)(r)(14) = 306
=> (22/7)r = 306/14
∴ r = (306/14)*(7/22) => 306/2*(1/22)
=> 306/44 => 6.95 cm ≈ 7 cm (for easier calculations)
(b) TSA of cone = πrl + πr²
=> πr(l + r)
=> (22/7)*7(14 + 7)
=> 22(21) => 462 cm² (approx)
(ii) (a) LSA of cylinder = 2πrh
h = 5 cm
=> 2πrh = 94.2 cm
=> πrh = 47.1 cm (Dividing whole equation by 2)
=> (3.14)(r)(5) = 47.1
=> 5r = 47.1/3.14 =>15
=> 5r = 15
∴ r = 15/5 => 3 cm
(b) Volume of cylinder = πr²h
=> (3.14)(3)²(5)
=> (3.14)(9)(5)
=> (3.14)(45) => 141.3 cm³