th STD8 Subject Mathematics VOLUME AND SURFACE AREA

th STD-8 Subject : Mathematics VOLUME AND SURFACE AREA Presented by : Mrs. Urmode A. R.

c CURVED SURFACE r CYLINDER h o r BASE A cylinder has altogether three surfaces. Of these, two surfaces are flat and circular. the remaining surface is curved. This is called the curved surface of the cylinder. The two flat circular surfaces have equal radii. The radius has been shown as ‘r’. The length of the line segment joining the centres C and O is called the height of the cylinder. It is shown as ‘h’ in the figure.

VOLUME OF CYLINDER The following formula is used to calculate the volume of a cylinder. Volume of cylinder=area of base x height If the radius of the base of cylinder is‘rʹand its height is h, then, VOLUME OF CYLINDER=лr²h If then value of л is not given, take л= ²²/₇ Curved surface of a cylinder =2 лrh Total surface area of cylinder=2 лr(h+r)

CYLINDRICAL OBJECTS

Example: 1 If the radius of the base of a cylinder is 7 cm and height is 15 cm, what is its volume? VOLUME OF CYLINDER= лr²h = ²²/₇x 7 x 7 x 15 =22 x 7 x 15 =2310 cu cm

Example: 2 The height of a cylindrical tank is 1 m and its diameter is 70 cm. How many litres of water can it hold? (1000 cu cm=1 litre ) Here, r=⁷⁰/₂=35 cm, h=1 m =100 cm Volume of tank = лr²h = ²²/₇x 35 x 100 = 22 x 5 x 35 x 100 =385000 cu cm 1000 cu cm =1 litre 385000 cu cm=³⁸⁵⁰⁰⁰/₁₀₀₀litre=385 litres ∙˙∙The tank will hold 385 litres of water.

Home Work 1)A cylinder has a base of radius 5 cm and height of 21 cm. What is its volume 2)The volume of a cylinder is 2512 cu cm and its height is 12. 5 cm. Find the radius of its base(л=3. 14) 3. 14 3)The circumference of the base of a cylinder is 132 cm. its height is 25 cm. What is the volume of the cylinder.

CONE OBJECTS

CONE Seg OA(h)is the height of the cone. Seg AP(r)is the radius of the base. Seg (l)is the slant height of the cone. o The angle between the height of the cone and a radius of the base is a right angle. A P Volume of a cone = ⅓ x area of base x height. Volume of cone=⅓ лr²h

Example: 1 The height of a cone is 14 cm and the radius of its base is 3 cm. What is its volume? Given h = 14 cm , r = 3 cm Volume of cone=⅓ лr²h = ⅓x²²/₇x 3 x 3 x 14 = 22 x 3 x 2 =132 cu cm. Hence , volume of given cone is 132 cu. cm.

Example : 2 The radius of the base of a cone is 5 cm and its slant height is 13 cm. Find its volume of the cone. (л=3. 14) Given : r : 5 cm , l : 13 cm l² = r² + h² 13² = 5²+h² 169 - 5 = h² ∙˙∙ 12 = h , л : 3. 14 volume of cone = ⅓ лr²h = ⅓ x 3. 14 x 5 x 12 = ⁹⁴² /₃ =314 cu cm. Hence , volume of given cone is 314 cu. cm.

Solve 1)Find the volume of a cone of height 7 cm and a radius of base 9 cm. Home - work Solve exercise 76.

SPHERE VOLUME OF SPHERE The point in the interior of the sphere equidistant from all points on its surface is called the centre of the sphere. The length of the segment joining the centre of the sphere to any point on its surface is called the radius of the sphere. It is represented by the letter ‘r’ VOLUME OF SPHERE=⁴/₃лr³

Example: If the radius of a ball Is 2. 1 cm, What is its volume. VOLUME OF SPHERE=⁴/₃лr³ =⁴/₃x²²/₇x 201 x 2. 1 =38. 808 cu cm

HOME WORK 1)The radius of a sphere is 30 cm, what is its volume? (л=3. 14) 2)The volume of a sphere is 36000 л cu cm. What is its radius. 3)Find the surface area of sphere of the following radii. 1)r=7 cm 2)r=10. 5 cm 3)r=10 cm (л=3. 14) 4)r=42 m