Question

The bottom part of this block is a rectangular prism. The top part is a square pyramid. You want to cover the block entirely with paper. How much paper do you need?

Answer 1

Answer:

Total paper required = 165 cm²

Step-by-step explanation:

Paper required to cover the entire block = (Surface area of the prism at the base - area of the top of the prism) + Lateral surface area of the pyramid

Surface area of the rectangular prism = 2(lb + bh + hl)

(here l, b, h are the length, width and height respectively)

                                                               = 2(5×5 + 5×4 + 4×5)

                                                               = 2(25 + 20 + 20)

                                                               = 2×65

                                                               = 130 cm²

Area of the top of the prism = (side)²

                                              = 5²

                                              = 25 cm²

Lateral area of the square pyramid = 4 × Area of one lateral side

                                                          = 4 × $[\frac{1}{2}(\text{Base})(\text{Height})]$

                                                          = 4 × $[\frac{1}{2}(5)(6)]$

                                                          = 60 cm²

Total paper required = (130 - 25) + 60

                                   = 105 + 60

                                   = 165 cm²