Question

1. A closed cylindrical tank of height 1.4 m. and radius of the base is 56 cm. is
made up of a thick metal sheet. How much metal sheet is required (Express in
square meters)
2. The volume of a cylinder is 308 cm. Its height is 8 cm. Find its lateral surface area and
total surface area.
3. A metal cuboid of dimension 22 cm. x 15 cm. x 7.5 cm. was melted and cast into a
cylinder of height 14 cm. What is its radius?
4. An overhead water tanker is in the shape of a cylinder has capacity of 616 litres. The
diameter of the tank is 5.6 m. Find the height of the tank.
R
5. A metal pipe is 77 cm. long. The inner diameter of a cross section is 4 cm.,
the outer diameter being 4.4 cm. (see figure) Find its
(1) inner curved surface area
(m) outer curved surface area
(1) Total surface area.​

Answer 1

Answer:

1.) Height = h =1.4 m

Radius = 56 cm = 0.56 m

So the Metal sheet required to make cylindrical tank are = total surface area of cylindrical tank which is equal to 2r(r+h)

=2×22/7×0.56(0.56+1.4)

=2×22×0.08×1.96

=6.8992 square meters.

3) Given a metal cuboid of dimension length 22 cm breadth 15 cm and height is 7.5 cm

Then volume of cuboid =22×15×7.5=2475cm 3

If we melt this cuboid and cast in the cylinder of height 14cm

Then the volume of cuboid =volume of cylinder

Let r is a radius of a cylinder

Then volume of cylinder =πr 2 h= 722 ×r 2 ×14

∴ 722

×r 2 ×14=2475

⇒r 2 = 22×142475×7

=56.25

⇒r=7.5cm