In this page volume solution3 we are going to see solution of each questions of the worksheet volume worksheet1.

**Question 7**:

A rectangular sheet of metal foil with dimension 66 cm x 12 cm is rolled to form a cylinder of height 12 cm. Find the volume of the cylinder.

**Solution:**

Length of metal sheet = 66 cm

Width of sheet = 12 cm

Now the metal sheet is in the form of cylinder. Here height of the cylinder is also 12 cm. Now 66 cm is to be considered as circumference of the base of the cylinder.

circumference of the base of the cylinder = 66 cm

2 Π r = 66

2 **x** (22/7) **x **r = 66

r = 66 **x **(1/2) **x** (7/22)

r = 3 **x **(1/2) **x** (7)

r = 21/2

r = 10.5 cm

Volume of the right circular cylinder = Π r² h

= (22/7)** x** (10.5)² **x** 12

= (22/7) **x** (10.5) **x**(10.5) **x** 12

= (22) **x** (1.5) **x **(10.5) **x** 12

= 4158 cm³

**Volume of the the right circular cylinder = 4158 cm³**

**Question 8**:

A lead pencil is in the shape of right circular cylinder. The pencil is 28 cm long and its radius is 3 mm. If the lead is of radius 1 mm,then find the volume of the wood used in the pencil.

**Solution:**

Height of the pencil = 28 cm

Outer radius (R) = 3 mm

Inner radius (r) = 1 mm

Now we have to change the units from mm to cm. For that we have to divide it by 10.

R = 3/10 = 0.3 cm

r = 1/10 = 0.1 cm

To find the volume of the wood used to make that pencil,simply we can find the volume of the pencil.Pencil is in the shape of hollow cylinder

Volume of hollow cylinder = Π h (R² - r²)

= (22/7) **x** 28 **x **(0.3² - 0.1²)

= (22) **x** 4 **x **(0.09 - 0.01)

= (22) **x** 4 **x **(0.08)

= 7.04 cm³

**Volume of wood used in the pencil = 7.04 cm³**

volume solution3 volume solution3

- Area
- Curved Surface Area
- Total Surface Area
- Volume
- Cylinder
- Conoid (Cone)
- Sphere
- Problems on Curved Surface Area
- Problems on Total Surface Area
- Problems on Volume
- Formulas For Shapes
- Perimeter of Sector
- Perimeter of Sector Worksheets
- Length of Arc
- Practice questions on length of arc
- Perimeter of square
- Perimeter of Parallelogram
- Perimeter of Rectangle
- Perimeter of a Triangle
- Area of a Circle
- Area of Semicircle
- Area of Quadrant
- Area of a Sector
- Area of a Triangle
- Area of Equilateral Triangle
- Area of Scalene Triangle
- Area of Square
- Area of Rectangle
- Area of Parallelogram
- Area of Rhombus
- Area of Trapezium
- Area of Quadrilateral
- Area Around Circle
- Path Ways
- Combined Figures