The lower portion of a haystack is an inverted cone frustum and upper part is a cone find the lateral surface area and the volume of the haystack
π=3.14
Answers
Answer:
The lateral surface area of haystack = 3328.4 cm²
The volume of the haystack = 16729.92 cm³
Step-by-step explanation:
Here, radius of cone , r = 20 cm
height of cone ,h = 15 cm
Thus, lateral height of cone ,l = √r²+h²
= √20²+15²
= √625 = 25 cm
upper radius of frustum , R = 20 cm
lower radius of frustum , R1 = 8 cm
Height of frustum , H = 16 cm
Lateral height of frustum, L = √[(R - R1)² + H²]
= √[(20-8)² + 16²]
= √(144 + 256)
= √400 = 20 cm
Thus, lateral surface area of haystack = curved surface area of cone + curved surface area of frustum
= πrl + π(R + R1) * L
= [3.14 * 20 * 25] + 3.14 * (20 + 8) * 20
= 1570 + 1758.4
= 3328.4 cm²
Volume of haystack = volume of cone + volume of frustum
= 1/3 * π * r² * h + 1/3 * π * (R² + R1² + R * R1) * H
= 1/3 * 3.14 * 20² * 15 + 1/3 * 3.14 * (20² + 8² + 20 * 8) * 16
= 6280 + 10449.92
= 16729.92 cm³