Question

The surface area of a sphere is 394.24 cm². If its radius is decreased by 25%, what will be the decrease in the surface area ?
Solution:- ?
Answer for Confirmation 172.48 cm².
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Answer 1

Answer:

★ Decrease = 172.48cm² ★

Step-by-step explanation:

Given:

• Surface Area of sphere is 394.24 cm²
• Radius is decreased by 25%

To Find:

• Total decrease in Surface Area of sphere

Solution: Surface Area of sphere is 4πr²

→ 394.24 = 4πr²

→ 394.24 = 4 x 22/7 x r² [ π = 22/7 ]

→ 394.24 = 88/7 x r²

→ (394.24 x 7 / 88) = r²

→ 2759.68/88 = r²

→ 31.36 = r²

→ √31.26 = r

→ 5.6 = r

Hence, Radius of Sphere is 5.6 Cm

★ Decreasing 25% of radius ★

→ New Radius of Sphere r¹ = r ( r – 25/100)

→ r¹ = 5.6( 5.6 – 1/4)

→ r¹ = 5.6 – 1.4

→ r¹ = 4.2 cm

So, The new Surface Area of sphere will be 4π(r¹)²

→ 4 x 22/7 x (4.2)²

→ 4 x 22/7 x 4.2 x 4.2

→ 1552.32/7

→ 221.76 Cm²

∴ Decrease in Surface area= ( Original surface area – New surface area )

→ Decrease = (394.24 – 221.76) cm²

→ 172.48 cm²

Hence, The Decrease in Surface area will be 172.48 cm²

Answer 2

||✪✪ QUESTION ✪✪||

The surface area of a sphere is 394.24 cm². If its radius is decreased by 25%, what will be the decrease in the surface area ?

|| ✰✰ ANSWER ✰✰ ||

we know That, surface Area of Square is 4πr² .

Given Surface Area is = 394.24cm².

So,

→ 4πr² = 394.24

→ 4* (22/7) * r² = 394.24

→ r² = (394.24*7/88)

→ r² = 31.36

Square - Root both sides ,

→ r = 5.6cm.

________________

Now, Given That, Radius is Decreased by 25% .

So,

→ New Radius = (5.6*75)/100 = 4.2cm.

Now,

→ New Surface Area = 4 * (22/7) * (4.2)² = 88 * 0.6 * 4.2 = 221.76cm².

________________

So,

→ Decrease in Surface Area = 394.24 - 221.76 = 172.48cm²

Hence, decrease in the surface area will be 172.48cm² .