lwlhwh SA = 2lw + 2lh +2wh SA = 2( 5.4 )( 2.8 )+ 2( 5.4 )( 1.5 )+ 2( 2.8 )( 1.5 ) SA = SA = 54.8 cm 2 or 54.8 sq cm SA = ≈ 54.8 cm 2 or 54.8 sq cm Surface Area of Rectangular Prisms Example: Jeff bought his mom a box of chocolates for Mother’s Day (aww). If the box is rectangular- prism-shaped with a length of 5.4 cm, a width of 2.8 cm, and a height of 1.5 cm, how much gift wrap will he need to wrap it up? 5.4 cm 1.5 cm 2.8 cm m/maths/nets/rectangular_ prism/rectangular_prism_ne t.gif

SA= 2πrh + 2 πr 2 SA= 2( π)( 0.9 )( 3.1 ) + 2( π)( 0.9 )( 0.9 ) SA = SA ≈ 22.6 ft 2 or 22.6 sq ft SA = ≈ 22.6 ft 2 or 22.6 sq ft Surface Area of Cylinders Example: Jackie has an old, aluminum garbage can that she wants to repaint. If the garbage can is cylinder-shaped, with a diameter of 1.8 ft and a height of 3.1 ft, how much paint will she need? 1.8 ft 3.1 ft om/maths/nets/cylinder/ cylinder_sm.gif

V = lwh V =(1.2 )( 1.2 )( 1.2 ) Volume of Rectangular Prisms Example: Bud has a cube- shaped container that he fills with compost. If the container’s length is 1.2 m long, how much compost will it take to fill it up? 1.2 m V = 1.7 m 3 or 1.7 cubic meters V = ≈ 1.7 m 3 or 1.7 cubic meters V lwh

V = πr 2 h V =( π )( 0.2 )( 0.2 )( 1.9 ) Volume of Cylinders Example: Wilma has a rain gauge that is shaped like a cylinder. It’s 1.9 yd tall and has a radius of 0.2 yd. What is the capacity of Wilma’s rain gauge? 0.2 yd 1.9 yd V = ≈ 0.2 yd 3 or or 0.2 cubic yards 0.2 cubic yards

Changing Volume Cleveland’s moving, so he’s buying boxes. There’s a small and a extra-large. All dimensions (length, width, height) are 4 times longer on the extra-large box. How much more will the extra-large box hold? To find the change in volume, use this formula: scale factor () Since each dimension is 4 times bigger, the scale factor is 4. sf sf 4 And, since all 3 dimensions changed, the exponent is # of dimensions changed changed The extra-large box holds 64 times more than the small. When he compares the small to the medium, he finds only the length is 4 times longer. How much more will the medium box hold? The medium box holds 4 times more than the small. 16 When he compares the small to the large, he finds the length and width are 4 times longer. How much more will the large box hold? 4 2 The large box holds 16 times more than the small.

Changing Surface Area For Valentine’s Day, Neil bought Meg a little jewelry box, and a huge box of chocolates. All dimensions of the huge box of chocolates are 5 times longer than the little jewelry box. How much more wrapping paper will he need for the huge box of chocolates? To find the change in surface area, use this formula: scale factor 2 Since each dimension is 5 times bigger, the scale factor is 5. sf sf The huge box of chocolates needs 25 times more wrapping paper. All the dimensions of large trunk are 3 times longer than a small trunk. How much more stain is needed to cover the large trunk? The large one needs 9 times more stain. 10,000 All the dimensions of a big sugar cube are 100 times longer than one grain of sugar. How much more surface does the big one have? We’ll only solve surface area problems in which all dimensions change by the same factor. There’s no easy formula when only 1 or 2 dimensions are changed. The large one has 10,000 times more surface.