A solid is in the form of a right circular cylinder with hemispherical ends. The total length of the solid is 42 cm. The diameter of the cylinder is half of its height. The surface area (in cm2) of the solid is:

Given:

Total length of the solid = 42 cm

Diameter of the cylinder = 1/2 of its height

Formula used:

Let height of the cylinder = h

Then, diameter = h/2, so radius (r) = h/4

Total length = height of the cylinder + 2 × radius of hemisphere

Curved Surface Area (CSA) of cylinder = 2πrh

Curved Surface Area of 2 hemispheres = 2 × 2πr²

Total Surface Area = CSA of cylinder + CSA of hemispheres

Calculation:

⇒ 42 = h + 2 × (h/4)

⇒ 42 = (3h/2)

⇒ h = 28 cm

⇒ r = h/4 = 28/4 = 7 cm

⇒ CSA of cylinder = 2 × 22/7 × 7 × 28

⇒ = 1232 cm²

⇒ CSA of hemispheres = 2 × 2 × 22/7 × 7²

⇒ = 616 cm²

⇒ Total Surface Area = 1232 + 616

⇒ = 1848 cm2

∴ The surface area of the solid is 1848 cm².