The radii of ends of a frustum are 14 cm and 6 cm respectively and its height is 6 cm. Find its
i) curved surface area
ii) total surface area.
iii ) volume (π= 3.14)
Answers
Answer:
The radii of ends of a frustum are 14 cm and 6 cm respectively and its height is 6 cm. (π= 3.14) its
i) curved surface area 628 cm²
ii) total surface area. 1356.48 cm²
iii ) volume 1984.48 cm³
Step-by-step explanation:
if we extend it till a point it become cone
then we have two cones
Larger cone
with radius = 14 cm
height = 6 + x
Smaller cone
radius = 6
height = x
using similar triangle
6/14 = x/(6+x)
=> 36 + 6x = 14x
=> x = 9/2 cm
Larger cone height = 6 + 9/2 = 21/2 cm
Small cone height = 9/2 cm
Volume = (1/3)πR²h
Volume = Larger cone volume - small cone volume
= (1/3)3.14* 14² * (21/2) - (1/3)3.14* 6² * (9/2)
= 2154.04 - 169.56
= 1984.48 cm³
Slanted large cone Height = √((21/2)² + 14²) = 17.5 cm
Slanted small cone Height = √((9/2)² + 6²) = 7.5 cm
Curved Surface area = πRL ( L - slanted height)
Curved Surface area = Large cone curved surface area - Smaller cone curved surface area
Curved Surface area = 3.14 * 14 * 17.5 - 3.14 * 6 * 7.5
= 769.3 - 141.3
= 628 cm²
Total surface area = Curved surface area + π14² + π6²
= 628 + 3.14(196 + 36)
= 628 + 728.48
= 1356.48 cm²