III. Surface Area Read the problems carefully. Write the formula then solve. 1. A pyramid has a square base of side 15cm and a height of 14 cm. Find the surface area of the pyramid. 2. The radius of the circular base of a cylindrical tank is 0.7 m and its height is 5 m. Find its surface area. 3. John is playing with a ball with radius of 30 cm. Find the surface area of the ball. 4. A certain music box ha the shape of a cube. Each side of the music box is 15 cm long. What is the surface area of the box? 5. Find the amount of tin needed to make a milk tin can that has a radius of 2.5 cm and a height of 5cm.
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1. Formula: Surface Area of Pyramid = base area + (0.5 x perimeter of base x slant height)
Solution: Base area = 15^2 = 225 sq cm
Perimeter of base = 4 x 15 = 60 cm
Slant height = sqrt(14^2 + 7.5^2) = 16.06 cm (using Pythagorean theorem)
Surface Area = 225 + (0.5 x 60 x 16.06) = 642.9 sq cm
2. Formula: Surface Area of Cylinder = 2πr^2 + 2πrh
Solution: Surface Area = 2π(0.7)^2 + 2π(0.7)(5) = 18.47 sq m
3. Formula: Surface Area of Sphere = 4πr^2
Solution: Surface Area = 4π(30)^2 = 11,310 sq cm
4. Formula: Surface Area of Cube = 6a^2 (where a is the length of one side)
Solution: Surface Area = 6(15)^2 = 1,350 sq cm
5.Formula: Surface Area of Cylinder = 2πr^2 + 2πrh (where r is the radius and h is the height)
Volume of Cylinder = πr^2h
Solution: Surface Area = 2π(2.5)^2 + 2π(2.5)(5) = 65.98 sq cm
Volume = π(2.5)^2(5) = 98.17 cu cm (rounded to two decimal places)
The amount of tin needed will be equal to the volume of the can, which is 98.17 cu cm.
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