A wooden article was made by scooping out a hemisphere from each end of a solid cylinder, as shown below. If the height of the cylinder is 10 cm and its base is of radius 3.5 cm. Find the total surface area of the article

OR

A heap of rice is in the form of a cone of base diameter 24 m and height 3.5 m. Find the volume of the rice. How much is canvas cloth required just to cover the heap?

Given:

• Cylinder with height(h) 10cm and diameter(2r) 7cm

• Hemispheres cut from the top and bottom

Total Surface Area = Curved Surface Area of Cylinder + Curved Surface Area of 2 hemi - spheres

= CSA of Cylinder + Total Surface Area of a Sphere

CSA of Cylinder = 2πrh where “r” is the radius of cylinder

“h” is the height of the cylinder

TSA of Sphere = 4πr² where “r” is the radius of the sphere

So,

Total Surface Area of the Article = 2πrh + 4πr²

= 2π(3.5)(10) + 4π(3.5)²

= 119π sq. cm

OR

Given:

• Height of Cone(h) = 3.5m

• Radius of the base(r) = 12m

The volume of the cone

where “r” is the radius, “h” is the height of the cone

= 168π cu. metres

And, Curved Surface Area of the Cone = πrl

where “l” is the slant height of the cone

Now,

(using the Pythagoras theorem)

= 12.5m

CSA of Cone = π(12)(12.5)

= 150π sq. metres

So, 168π m³ is the volume of the rice and, 150π m² of canvas cloth is required to cover the heap