A sphere has the same curved surface as the total surface area of cylinder of height 4 cm and diameter of base 8 cm. The radius of the sphere is
$2 c m$
$3 c m$
$4 c m$
$6 c m$

Question

A sphere has the same curved surface as the total surface area of cylinder of height 4 cm and diameter of base 8 cm- The radius of the sphere is 2 cm3  cm4 cm6 cm

Toppr Admin · Accepted Answer

Let the radius of the sphere be r- Then curved surface of sphere -4-x3C0-r2Total surface of cylinder-2-x3C0-r-r-h-2-x3C0-xD7-4-xD7-4-4-64-x3C0-x2234-4-x3C0-r2-64-x3C0-x2234-r-4 cm

A sphere has the same curved surface as the total surface area of cylinder of height 4 cm and diameter of base 8 cm. The radius of the sphere is 2 cm3 cm4 cm6 cm

Let the radius of the sphere be r. Then curved surface of sphere =4πr2Total surface of cylinder=2π.r.(r+h)=2π×4×(4+4)=64π∴4πr2=64π∴r=4 cm

A sphere has the same curved surface as the total surface area of cylinder of height 4 cm and diameter of base 8 cm. The radius of the sphere is
$2 c m$
$3 c m$
$4 c m$
$6 c m$

Let the radius of the sphere be $r$ . Then curved surface of sphere $= 4 π r^{2}$
Total surface of cylinder
$= 2 π . r . (r + h)$
$= 2 π \times 4 \times (4 + 4) = 64 π$
$∴ 4 π r^{2} = 64 π$
$∴ r = 4$ cm