NCERT Solutions for Class 10 Maths
Surface areas and Volumes,
NCERT Books for Session 2022-2023
CBSE Board and UP Board Others state Board
EXERCISE 13.4
Page No:257
Questions No:5
A metallic right circular cone 20 cm high and whose vertical angle is 60° is cut into two parts at the middle of its height by a plane parallel to its base. If the frustum so obtained be drawn into a wire of diameter 1/6 cm find the length of the wire.
Share
In ΔAEG,
EG/AG = tan 30°
⇒ EG/10 = 1/√3
⇒ EG = 10/√3
In ΔABD,
BD/AD = tan 30°
⇒ BD/20 = 1/√3
⇒ BD = 20√3
Radius of upper part of frustum (r₁) = 10/√3
Radius of lower part of frustum (r₂) = 20/√3
Height of frustum (h) = 10 cm
Volume of frustum = 1/3πh(r₁² + r₂² + r₁r₂)
= 1/3π × 10 × [(10/√3)² + (20/√3)² + 10/√3 × 20/√3]
= 1/3 × 22/7 × 10 × (100/3 + 400/3 + 200/3)
= 1/3 × 22/7 × 10 × (700/3) = 22000/9 cm³
Radius of wire (r) = 1/2 × 1/16 = 1/32 cm
Let the lenght of wire = l
Volume of wire = area of cross- section of wire × length of wire
= (πr²) (l)
= π(1/32)²× l
Volume of frustum = Volume of wire
⇒ 22000/9 = π(1/32)² × l
⇒ 22000/9 = 22 /7 × 1/1024 × l
⇒ l = 22000/9 × 7/22 × 1024
= 796444.44 cm
7964. 44 m
Hence, the length of wire is 7964.44 m.
Get Hindi Medium and English Medium NCERT Solution for Class 10 Maths to download.
Please follow the link to visit website for first and second term exams solutions.
https://www.tiwariacademy.com/ncert-solutions/class-10/maths/chapter-13/