SURFACE AREAS

AND VOLUMES

• Sum based on Cuboid and Cone

Q. A pen stand made of wood is in the shape of a cuboid with four

conical depressions to hold pens. The dimensions of the cuboid are

15 cm by 10 cm by 3.5 cm. The radius of each of the depressions is

0.5 cm and depth is 1.4 cm. Find the volume of wood in the entire stand.

0.5cm

Volume of wood in the stand =

1.4cm

What is the formula to find volume of a cuboid?

Volume of cuboid (V₁) –

l b h₁

What is the formula to find volume of a cone?

Volume of 4 cones (V₂)

✔

✔

✔

✔

✔

Vol. of the cuboid(V₁) = l b h₁

Vol. of the 4 cones(V₂)

=

Sol.

= 15 ×

= 525 cm³

4

×

×

× 0.5

× 0.5

× 1.4

4

×

πr²h₂

=

10 ×

3.5

0.5cm

15 cm

10cm

3.5cm

1.4cm

Q. A pen stand made of wood is in the shape of a cuboid with four

conical depressions to hold pens. The dimensions of the cuboid are

15 cm by 10 cm by 3.5 cm. The radius of each of the depressions is

0.5 cm and depth is 1.4 cm. Find the volume of wood in the entire stand.

Vol. of wood in the entire stand =

Volume of cuboid (V₁) –

l b h₁

Volume of 4 cones (V₂)

= 15 ×

35

∴ Vol. of the cuboid(V₁)

×

×

×

4

×

×

=

∴ Vol. of the 4 cones(V₂)

2

=

4 ×

3

22

× 5

× 5

× 2

× 1000

Q. A pen stand made of wood is in the shape of a cuboid with four

conical depressions to hold pens. The dimensions of the cuboid are

15 cm by 10 cm by 3.5 cm. The radius of each of the depressions is

0.5 cm and depth is 1.4 cm. Find the volume of wood in the entire stand.

0.5cm

15 cm

10cm

3.5cm

1.4cm

Sol.

Vol. of wood in the entire stand =

Volume of cuboid (V₁) –

Volume of 4 cones (V₂)

Vol. of the 4 cones(V₂)

=

4 ×

3

22

× 5

× 5

× 2

× 1000

=

4400

3

× 1000

=

44

3

× 10

=

14.66

10

=

1.47 cm³

∴ Vol. of the 4 cones(V₂)

Volume of the wood

in the entire stand

= V₁

=

Volume of the wood in the entire stand is 523.53 cm³

V₂

–

525

– 1.47

= 523.53 cm³

∴

Q. A pen stand made of wood is in the shape of a cuboid with four

conical depressions to hold pens. The dimensions of the cuboid are

15 cm by 10 cm by 3.5 cm. The radius of each of the depressions is

0.5 cm and depth is 1.4 cm. Find the volume of wood in the entire stand.

0.5cm

15 cm

10cm

3.5cm

1.4cm

Vol. of wood in the entire stand =

Volume of cuboid (V₁) –

Volume of 4 cones (V₂)

Sol.