Question

curved surface area of solid hemisphere wooden block is 122 cm find its total surface area​

Answer 1

The total surface area of the solid hemisphere wooden block is  183 cm².

Step-by-step explanation:

The curved surface area of solid hemisphere wooden block = 122 cm

We know that,

The Curved Surface Area of the solid hemisphere = 2πr² ... where r is the radius of the solid hemisphere

∴ 2πr² = 122

⇒ 2 × $\frac{22}{7}$ × r² = 122

⇒ r² = [122 × 7]  / [2 × 22]

⇒ r² = 854 / 44

⇒ r = √19.40

⇒ r = 4.4 cm

Now,

The formula of the total surface area of a solid hemisphere is given by,

T.S.A of a solid hemisphere = 3πr²

Substituting the value of r in the above formula, we get

T.S.A of the solid hemisphere = 3 × $\frac{22}{7}$ × 4.4² = 182.53 cm² ≈ 183 cm²

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Answer 2

Given: curved surface area of solid hemisphere is 122 cm.

To find: Total surface area of solid hemisphere.

Solution:

• Since we know the formula for Curved Surface Area of the solid hemisphere = 2πr²

• So by equating the area given, with the formula we can find the radius of the hemisphere.

              2πr² = 122

              πr² = 122/2

              r² = 61/ 3.14

              r² = 19.4

              r = 4.4 cm.

• So now, we have got the radius of the hemisphere, we will put it in the formula of total hemisphere = 3πr²

             = 3π(4.4)²

             = 3 x 3.14 x 4.4 x 4.4

             = 182.53 cm²

Answer:

• So the total surface area of the wooden block is 182.53 cm sq.