A solid metallic sphere of radius 6 c m is melted and made into a solid cylinder of height 32 c m . Find the curved surface area of the cylinder. (Take π = 3 . 1 )

Radius of metallic sphere R = 6 c m Height of cylinder h = 32 c m Volume of cylinder = Volume of metallic sphere π r 2 h = 4 3 π R 3 r 2 × 32 = 4 3 × 6 3 r 2 = 4 × 6 × 6 × 6 3 × 32 r 2 = 9 r = 3 c m Then, curved surface area of the cylinder = 2 π r h = 2 × 3 . 1 × 3 × 32 = 595 . 2 c m 2

HARD

10th ICSE

IMPORTANT

Earn 100

A hollow sphere of internal and external diameter $4 cm$ and $8 cm$ respectively is melted into a cone of base diameter $8 cm$ . Find the height of the cone.

Important Questions on Mensuration

HARD

10th ICSE

IMPORTANT

Understanding ICSE Mathematics Class 10>Chapter 17 - Mensuration>Exercise 17.5>Q 11

A hollow sphere of internal and external diameter

4 cm

and

8 cm

respectively is melted into a cone of base diameter

8 cm .

Find the height of the cone.

HARD

10th ICSE

IMPORTANT

Understanding ICSE Mathematics Class 10>Chapter 17 - Mensuration>Exercise 17.5>Q 12

A cylindrical can of internal diameter

21 cm

contains water. A solid sphere whose diameter is

10.5 cm

is lowered into the cylindrical can. The sphere is completely immersed in water. Calculate the rise in water level, assuming that no water overflows.

MEDIUM

10th ICSE

IMPORTANT

Understanding ICSE Mathematics Class 10>Chapter 17 - Mensuration>Exercise 17.5>Q 13

There is a water to the height of

14 cm

in a cylindrical glass jar of radius

8 cm

. Inside the water there is a sphere of diameter

12 cm

completely immersed. By what height will the water go down when the sphere is removed ?

HARD

10th ICSE

IMPORTANT

Understanding ICSE Mathematics Class 10>Chapter 17 - Mensuration>Exercise 17.5>Q 14

A vessel in the form of an inverted cone is filled with water to the brim. Its height is

20 cm

and diameter is

16.8 cm

. Two equal solid cones are dropped in it so that they are fully submerged. As a result, one third of the water in the original cone overflows. What is the volume of each of the solid cone submerged?

HARD

10th ICSE

IMPORTANT

Understanding ICSE Mathematics Class 10>Chapter 17 - Mensuration>Exercise 17.5>Q 15

A solid metallic circular cylinder of radius

14 cm

and height

12 cm

is melted and recast into small cubes of edge

2 cm

. How many such cubes can be made from the solid cylinder?

EASY

10th ICSE

IMPORTANT

Understanding ICSE Mathematics Class 10>Chapter 17 - Mensuration>Exercise 17.5>Q 16

How many shots having diameter $3 cm$ can be made from a cuboidal lead solid of dimensions $9 cm \times 11 cm \times 12 cm$ ?

MEDIUM

10th ICSE

IMPORTANT

Understanding ICSE Mathematics Class 10>Chapter 17 - Mensuration>Exercise 17.5>Q 17

A solid metal cylinder of radius

14 cm

and height

21 cm

is melted down and recast into spheres of radius

3.5 cm

. Calculate the number of spheres that can be made.

MEDIUM

10th ICSE

IMPORTANT

Understanding ICSE Mathematics Class 10>Chapter 17 - Mensuration>Exercise 17.5>Q 18

A metallic sphere of radius

10.5 c m

is melted and recasted into small cones, each of radius

3.5 c m

and height

3 c m

. Find how many cones are obtained.

A hollow sphere of internal and external diameter 4 cm and 8 cm respectively is melted into a cone of base diameter 8 cm. Find the height of the cone.

Important Questions on Mensuration

Learn and Prepare for any exam you want !

A hollow sphere of internal and external diameter $4 cm$ and $8 cm$ respectively is melted into a cone of base diameter $8 cm$ . Find the height of the cone.