radii of ends of a frustum are 13 cm and 6 cm respectively and its height is 24 cm.
The radii of ends
Find its
(1) curved surface area
(2) total surface area
(3) volume
(π = 3.14)
Answers
Answer:
i) Curved Surface area of the frustum = 1287.53 cm²
ii) Total surface area = 1931.23 cm²
iii) Volume = 7348.197 cm³
Step-by-step explanation:
Given the radii of the bottom and top of the frustum, we can get the height of the smaller cone using the linear scale factor.
Linear Scale factor = 13/6
Let the height of the small cone at the top be x
The height of the big cone = x + 24
(x + 24)/x = 13/6
6(x + 24) = 13x
6x + 156 = 13x
13x - 6x = 156
7x = 156
x = 156/7
x = 22 2/7 cm
Height of big cone = 24 + 22 2/7 cm = 46 2/7 cm
The slant height of the big cone is:
l = √(13² + (46 2/7)²)
l = 40.08 cm
Slant height of the smaller cone = 6/13 × 40.08 = 18.50 cm
i) Curved surface area of the frustum
Curved surface area of a cone = πrl
Curved Surface area of the frustum = (3.14 × 13 × 40.08) - (3.14 × 6 × 18.50) = 1287.53 cm²
ii) Total surface area;
= (3.14 × 13²) + (3.14 × 6²) + (1287.53 ) = 1931.23 cm²
iii) Volume of the frustum
Volume of a cone = 1/3πr²h
Volume of the frustum = (1/3 × 3.14 × 13² × 46.29) - (1/3 × 3.14 × 6² × 22.29) = 7348.197 cm³
Answer:
I will give see in down with explaination