Algebra 1 Surface area of solid Figures CONFIDENTIAL

Warm Up 1) Calculate the volume of the Triangular prism with altitude = 7.6 cm , base = 11 cm and the height is = 15 cm. 627 cm3 2) The given cylinder has radius = 13 cm and the height = 16 cm. A cone of radius = 9 cm and height = 13 cm is cut from the cylinder. What is the volume of the remaining piece? 7388.42 cm3 3) If the volumes of two cubes are in the ratio 64 : 1, then what is the ratio of their edges? 4:1 4) The radius of a cylinder is decreased to 1/5th of the original radius. How many times will its height increase, if its volume remains the same? 25 times CONFIDENTIAL

The surface area of a rectangular solid is expressed in square units. The surface area of a solid figure is the sum of the areas of all faces of the figure. An area of study closely related to solid geometry is nets of a solid. Imagine making cuts along some edges of a solid and opening it up to form a plane figure. The plane figure is called the net of the solid. The surface area of a rectangular solid is expressed in square units. CONFIDENTIAL

Surface Area of solid figures In general, Surface Area of solid figures = 2 x area of the base +perimeter of the base x height If, B = area of the base P = perimeter of the base h = height SA = Surface Area Then, SA = 2B +Ph CONFIDENTIAL

If s is the length of one of its sides, then Cubes A cube is a three-dimensional figure with all edges of the same length. s s If s is the length of one of its sides, then SA = 2(s2) + (4s)s = 6s2 CONFIDENTIAL

Calculate the surface area of the cube with length of sides = 7 cm. Volume of the cube = 6s2 = 6 x (7)2 = 6 x 49 = 294 Surface Area of the cube = 294 cm2 CONFIDENTIAL

Triangular prism b a h c d a b h c d SA = 2( 1 ) + (b + c + d)h 2ab SA = ab + (b + c + d)h CONFIDENTIAL

Calculate the surface area of the regular triangular prism. 5 8 10 Surface area of the triangular prism = a x b + (b + c + d)h = 5 x 8 + (8 + 8 + 8) x 10 = 40 + 240 = 280 Surface area of the cuboid = 280 cm2 CONFIDENTIAL

Now you try! 1) The surface area of a cube is 294 ft2. Find the length of each edge. 7ft 2) Calculate the surface area of the given triangular prism. 645 units2 5 8 11 6 7 CONFIDENTIAL

Rectangular prism h h w w l l SA = 2B + Ph SA = 2(lw) + (2l + 2w)h CONFIDENTIAL

Calculate the surface area of the given rectangular prism. 8 4 7 Surface area of the rectangular prism = 2(lw) + (2l + 2w)h = 2(8 x 4) + (2 x 8 + 2 x 4) x 7 = 2 x 32 + (16 + 8) x 7 = 64 + 168 = 232 Surface area of the rectangular prism = 268 cm2 CONFIDENTIAL

Regular square prism h h s s SA = 2B + Ph SA = 2(s2) + (4s)h CONFIDENTIAL

Calculate the surface area of the given Regular square prism. 8 11 Surface area of the Regular square prism = 2(s2) + (4s)h = 2(8 x 8) + (4 x 8) x 11 = 2 x 64 + 32 x 11 = 128 + 352 = 480 Surface area of the regular square prism = 480 cm2 CONFIDENTIAL

Regular pentagonal prism h a s a h SA = 2(1ans) + nsh 2 SA = 2(1a)(5)s + 5sh 2 SA = 5as + 5sh CONFIDENTIAL

Calculate the surface area of the given Regular pentagonal prism. 8 9 6 Surface area of the Regular square prism = 5as + 5sh = 2 x 6 x 8 + 5 x 8 x 9 = 2 x 48 + 5 x 72 = 96 + 360 = 456 Surface area of the regular square prism = 456 cm2 CONFIDENTIAL

Now you try! 1) The surface area of a regular square prism is 294 ft2 and height 10 ft. Find the length of each edge of the base. 5.7ft 2) Calculate the surface area of the given Regular pentagonal prism. 180 sq units 4 6 3 CONFIDENTIAL

Regular triangular pyramid s l a s SA = B + n(1sl) 2 SA = 1as + (3)(1sl) 2 2 SA = 1as + 3sl 2 2 l = slant height CONFIDENTIAL

Calculate the surface area of the given Regular triangular pyramid. 5 4 6 Surface area of the Regular triangular pyramid = 1as + 3sl 2 2 = 1 x 4 x 6 + 3 x 6 x 5 2 2 = 18 + 45 = 63 Surface area of the regular triangular pyramid = 63 cm2 CONFIDENTIAL

Regular square pyramid h l SA = B + n(1sl) 2 SA = s2 + (4)(1sl) 2 SA = s2 + 2sl CONFIDENTIAL

Calculate the surface area of the given Regular square pyramid. 8 h 7 Surface area of the Regular square pyramid = s2 + 2sl =8 x 8 + 2 x 8 x 7 = 64 + 112 = 176 Surface area of the regular square pyramid = 176 cm2 CONFIDENTIAL

Now you try! 1) Calculate the surface area of the given Regular triangular pyramid. 103.5 sq units 5 8 9 2) Calculate the surface area of the given Regular square pyramid. 280 sq units 10 h 9 CONFIDENTIAL

Cylinder h r P r h SA = 2B + Ph SA = 2(Π r2) + (2 Π r)h CONFIDENTIAL

Calculate the surface area of the given cylinder. 5 8 Surface area of the cylinder = 2(Π r2) + (2 Π r)h =2 x (3.14 x 5 x 5 ) + (2 x 3.14 x 5 ) x 8 = 157 + 251.2 = 408.2 Surface area of the cylinder = 408.2 cm2 CONFIDENTIAL

Sphere r SA = 4 Π r2 CONFIDENTIAL

Calculate the surface area of the given sphere. 10 Surface area of the sphere = 4 Π r2 =4 x 3.14 x 10 x 10 = 1256 Surface area of the sphere = 1256 cm2 CONFIDENTIAL

1) Calculate the surface area of the given cylinder. 748 sq units Now you try! 1) Calculate the surface area of the given cylinder. 748 sq units 7 10 2) Calculate the surface area of the given sphere. 804.6 sq units 8 CONFIDENTIAL

Assessment 1) What is the perimeter of the floor, if the area of the four walls is equal to 2700 ft2 and its height is 12 ft? 225 ft 2) The perimeter of one face of a cube is 48 cm. What is its surface area? 864 sq cm CONFIDENTIAL

3) The base radius of a cylinder is 2 cm and its height is 5 cm 3) The base radius of a cylinder is 2 cm and its height is 5 cm. What is the resultant surface area of the cylinder, if the radius is increased by 2 times? 326.86 sq cm 4) Calculate the surface area of the given Regular triangular pyramid. 139.5 sq units 8 7 9 CONFIDENTIAL

5) Calculate the surface area of the given Regular pentagonal prism 5) Calculate the surface area of the given Regular pentagonal prism. 225 sq units 4.5 7 3 6) Calculate the surface area of the given Regular square pyramid. 133 sq units 7 h 6 CONFIDENTIAL

7) Calculate the surface area of the sphere with radius = 34 cm. 14519 7) Calculate the surface area of the sphere with radius = 34 cm. 14519.36 sq cm 8) The base area of a square pyramid is 49 in2. What is the surface area of the pyramid , if the slant height of the pyramid is 12 in? 217 sq in CONFIDENTIAL

9) A rectangular tin sheet of 44 in. long and 20 in 9) A rectangular tin sheet of 44 in. long and 20 in. broad is rolled along its length to form a cylinder by making the opposite edges just touch each other. What is the base radius of the cylinder formed? 5.49 in 10) What is the lateral area of a cube, if the area of each face of the cube is 16 ft2? 64 sq ft CONFIDENTIAL

10 7 3 5 11) The figure shows a rectangular prism with a cylinder which has been removed from it. What is the total surface area of the given solid? Round the answer to the nearest ten. 530 sq units CONFIDENTIAL

Let’s review In general, Surface Area of solid figures = 2 x area of the base +perimeter of the base x height If, B = area of the base P = perimeter of the base h = height SA = Surface Area Then, SA = 2B +Ph CONFIDENTIAL

If s is the length of one of its sides, then review Cubes A cube is a three-dimensional figure with all edges of the same length. s s If s is the length of one of its sides, then SA = 2(s2) + (4s)s = 6s2 CONFIDENTIAL

review Triangular prism b a h c d a b h c d SA = 2( 1 ) + (b + c + d)h 2ab SA = ab + (b + c + d)h CONFIDENTIAL

review Rectangular prism h l w h SA = 2B + Ph SA = 2(lw) + (2l + 2w)h CONFIDENTIAL

Regular pentagonal prism review Regular pentagonal prism s h a s a h SA = 2(1ans) + nsh 2 SA = 2(1a)(5)s + 5sh 2 SA = 5as + 5sh CONFIDENTIAL

Regular triangular pyramid review Regular triangular pyramid l a s l a s SA = B + n(1sl) 2 SA = 1as + (3)(1sl) 2 2 SA = 1as + 3sl 2 2 l = slant height CONFIDENTIAL

Regular square pyramid review Regular square pyramid l s s h l SA = B + n(1sl) 2 SA = s2 + (4)(1sl) 2 SA = s2 + 2sl CONFIDENTIAL

review Cylinder r P h h r SA = 2B + Ph SA = 2(Π r2) + (2 Π r)h CONFIDENTIAL

review Sphere r SA = 4 Π r2 CONFIDENTIAL

You did a great job today! CONFIDENTIAL