Maharashtra Board Class 9 Maths Part II Chapter 9 Surface Area and Volume PDF Download

Surface Area And Volume

Let's Recall

We have learnt how to find the surface area and volume of a cuboid, a cube and a cylinder, in earlier standard.

Cuboid

Length, breadth and height of a cuboid are l, b, h respectively.

(i) Area of vertical surfaces of a cuboid = 2(l + b) × h

Here we have considered only 4 surfaces into consideration.

(ii) Total surface area of a cuboid = 2(lb + bh + lh)

Here we have taken all 6 surfaces into consideration.

(iii) Volume of a cuboid = l × b × h

Cube

If l is the edge of a cube,

(i) Total surface area of a cube = 6l²

(ii) Area of vertical surfaces of a cube = 4l²

(iii) Volume of a cube = l³

Cylinder

Radius of cylinder is r and height is h.

(i) Curved surface area of a cylinder = 2πrh

(ii) Total surface area of a cylinder = 2πr(r + h)

(iii) Volume of a cylinder = πr²h

Teacher's Note

You see cuboid shapes everywhere in your home - like medicine boxes, books, and water tanks. Understanding these shapes helps you calculate how much space they need.

Exam Trick

Remember: Cuboid has 6 faces. When you want only vertical faces (like walls), use 4 faces. When you want total, use all 6 faces - just like your house has 4 walls plus floor and ceiling.

Points to Remember

Cuboid has length, breadth, and height as three different measurements.
Cube is special - all three sides are equal.
Cylinder is round like a pipe or tin can.
Surface area is like the outer covering or paint needed.
Volume is how much space is inside.

Let's Study

Surface area of a cone

Volume of a cone

Surface area of a sphere

Volume of a sphere

Practice Set 9.1

1. Length, breadth and height of a cuboid shape box of medicine is 20cm, 12 cm and 10 cm respectively. Find the surface area of vertical faces and total surface area of this box.

2. Total surface area of a box of cuboid shape is 500 sq. unit. Its breadth and height is 6 unit and 5 unit respectively. What is the length of that box ?

3. Side of a cube is 4.5 cm. Find the surface area of all vertical faces and total surface area of the cube.

4. Total surface area of a cube is 5400 sq. cm. Find the surface area of all vertical faces of the cube.

5. Volume of a cuboid is 34.50 cubic metre. Breadth and height of the cuboid is 1.5m and 1.15m respectively. Find its length.

6. What will be the volume of a cube having length of edge 7.5 cm ?

7. Radius of base of a cylinder is 20cm and its height is 13cm, find its curved surface area and total surface area. (π = 3.14)

8. Curved surface area of a cylinder is 1980 cm² and radius of its base is 15cm. Find the height of the cylinder. (π = \(\frac{22}{7}\))

Teacher's Note

Practice problems help you become better at math. When you solve these problems step by step, you understand the concept better - just like practising a game makes you better at it.

Exam Trick

Always write down what you are given and what you need to find. This helps you choose the correct formula. Like in a recipe, first read all ingredients before you start cooking.

Points to Remember

Read the question carefully two times.
Write down which measurements are given.
Choose the correct formula for what you need to find.
Do all calculations step by step.
Write the answer with the correct unit (cm, m, cubic cm, sq. cm).

Terms Related To A Cone And Their Relation

A cone is shown in the adjacent figure. Centre of the circle, which is the base of the cone, is O and A is the vertex (apex) of the cone. Seg OB is a radius and seg OA is perpendicular to the radius at O, means AO is perpendicular height of the cone. Slant height of the cone is the length of AB, which is shown by (l).

Triangle AOB is a right angled triangle.

By the Pythagoras' theorem

\[AB^2 = AO^2 + OB^2\]

\[l^2 = h^2 + r^2\]

That is, (slant height)² = (Perpendicular height)² + (Base radius)²

Surface Area Of A Cone

A cone has two surfaces : (i) circular base and (ii) curved surface.

Out of these two we can find the area of base of a cone because we know the formula for the area of a circle.

How to find the curved surface area of a cone ? How to derive a formula for it ?

Teacher's Note

A cone shape is seen in ice cream cones and traffic cones on roads. Understanding how to find its surface area helps in real life when you need to cover or paint these shapes.

Exam Trick

Remember: l² = h² + r². This is Pythagoras' theorem applied to cone. If you know any two values, you can always find the third one using this formula.

Points to Remember

A cone has a circular base and a curved surface.
The vertex is the sharp point at the top of the cone.
Height is always vertical (straight up).
Slant height is the distance along the curved surface.
Use l² = h² + r² to find any missing measurement.

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