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Two identical solid hemispheres of equal base radius r cm are stuck together along their bases. The total surface area of the combination is 6πr². Is the following statement true or false and justify your answer

Solution:

Given, two identical solid hemispheres of equal base radius r cm are stuck together along their bases.

We have to determine if the total surface area of the combination is 6πr².

By joining two identical solid hemispheres of equal radius along their bases, we get a sphere.

We know that,

Total surface area of the sphere = curved surface area of the sphere

Since sphere is a 3-D shape which has no face or edge

Total surface area of the sphere = 4πr².

Therefore, the given statement is false.

✦ Try This: Two identical solid hemispheres of equal base radius r cm are stuck together along their bases. The total surface area of the combination is kπr². Find k.

Given, two identical solid hemispheres of equal radius are joined together along their bases.

The total surface area of the combination is kπr².

We have to find the value of k.

When two hemispheres are joined we get a sphere.

Total surface area of the sphere = 4πr² -------------------------- (1)

Total surface area of the given combination = kπr² ------------ (2)

By comparing (1) and (2),

k = 4

Therefore, the value of k is 4.

☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 13

NCERT Exemplar Class 10 Maths Exercise 12.2 Problem 1

Two identical solid hemispheres of equal base radius r cm are stuck together along their bases. The total surface area of the combination is 6πr². Is the following statement true or false and justify your answer

Summary:

The statement “Two identical solid hemispheres of equal base radius r cm are stuck together along their bases. The total surface area of the combination is 6πr².” is false

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