Question 11 - CBSE Class 10 Sample Paper for 2022 Boards - Maths Standard [Term 2] - Solutions of Sample Papers for Class 10 Boards

Last updated at May 29, 2023 by Teachoo

The internal and external radii of a spherical shell are 3cm and 5cmrespectively. It is melted and recast into a solid cylinder of diameter 14cm, find the height of the cylinder. Also find the total surface area of the cylinder. ("Take 𝜋 = " 22/7)

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The internal and external radii of a spherical shell are 3cm and 5cm respectively. It is melted and recast into a solid cylinder of diameter 14cm, find the height of the cylinder. Also find the total surface area of the cylinder. ("Take 𝜋 = " 22/7)
Since spherical shell is melted into a cylinder ,
So,
Volume of spherical shell = Volume of cylinder
Volume of spherical shell
Internal Radius = r = 3 cm
External Radius = R = 5 cm
Volume of spherical shell = 4/3 𝜋𝑅3−4/3 𝜋𝑟3
= 𝟒/𝟑 𝝅(𝑹^𝟑−𝒓^𝟑)
= 4/3 𝜋(5^3−3^3)
= 4/3 𝜋(126−27)
= 𝟒/𝟑 𝝅 × 𝟗𝟖
Volume of cylinder
Given, Diameter = 14 cm
∴ Radius = r = 7 cm
Let height = h cm
Volume of cylinder = 𝜋𝑟2ℎ
= 𝜋×7^2×ℎ
= 49𝝅h
Now,
Volume of spherical shell = Volume of cylinder
𝟒𝝅/𝟑 × 𝟗𝟖=𝟒𝟗𝝅𝒉
4𝜋/3 × 98 ×1/49𝜋=ℎ
4/3 × 2 =ℎ
8/3 =ℎ
𝒉=𝟖/𝟑 cm
We also need to find find the total surface area of the cylinder
Total Surface Area of cylinder = 2𝜋𝑟ℎ+2𝜋r^2
= 𝟐𝝅𝒓(𝒉+𝒓)
Putting values
= 2 ×22/7 × 7 × (8/3+7)
= 2 × 22 × ((8 + 7 × 3)/3)
= 44 × ((8 + 21)/3)
= 𝟒𝟒 ×𝟐𝟗/𝟑
= 1276/3
= 425.33 cm2

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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