SURFACE AREAS

AND VOLUMES

• Sum based on Frustum of cone

Q. A fez, the cap used by the Turks, is shaped like the frustum of a

cone If its radius on the open side is 10 cm,

radius at the upper base is 4 cm and its slant height is 15 cm,

find the area of material used for making it.

Sol.

4 cm

10 cm

15 cm

r₁

=

10 cm,

r₂

=

4 cm,

l

=

15 cm

Area of material used =

CSA of (Frustum) +

What is the formula to find curved surface area of frustum?

πl (r₁ + r₂)

Area of top

✔

π r₂²

What is the formula to find area of top?

✔

✔

✔

Area of material used =

CSA of (Frustum) +

Area of top

Q. A fez, the cap used by the Turks, is shaped like the frustum of a

cone. If its radius on the open side is 10 cm,

radius at the upper base is 4 cm and its slant height is 15 cm,

find the area of material used for making it.

Sol.

r₁

=

10 cm,

r₂

=

4 cm,

l

=

15 cm

πl (r₁ + r₂)

π r₂²

CSA of (Frustum)

=

πl

(r₁ + r₂)

=

×

15

(10

+ 4)

=

×

15

× 14

2

=

22

×

15

× 2

=

660 cm²

∴ CSA of (Frustum)

×

Area of material used =

CSA of (Frustum) +

Area of top

Q. A fez, the cap used by the Turks, is shaped like the frustum of a

cone. If its radius on the open side is 10 cm,

radius at the upper base is 4 cm and its slant height is 15 cm,

find the area of material used for making it.

Sol.

r₁

=

10 cm,

r₂

=

4 cm,

l

=

15 cm

πl (r₁ + r₂)

π r₂²

Area of top

π r₂²

=

×

(4)²

=

×

=

16

=

∴ Area of top

cm²

Q. A fez, the cap used by the Turks, is shaped like the frustum of a

cone. If its radius on the open side is 10 cm,

radius at the upper base is 4 cm and its slant height is 15 cm,

find the area of material used for making it.

Sol.

r₁

=

10 cm,

r₂

=

4 cm,

l

=

15 cm

=

710.28cm²

=

∴ Area of material used making it is 710.28 cm²

Area of material used =

CSA of (Frustum) +

Area of top

πl (r₁ + r₂)

π r₂²

Area of material used =

CSA of (Frustum) +

Area of top

=

660

+

CSA of (Frustum) = 660 cm²