Question

Figure 2 shows a cuboid and a prism (not drawn to scale). Edges CD and BF have length 12 cm, and the diagonal BD has length 32 cm. The area A of the top of the prism is 96 cm2 and the perimeter p is 48 cm. area A is 96 cm2 perimeter p is 48 cm 12 cm 32 cm 12 cm Figure 2 Give your answers to each of the following to two significant figures. (i) Use Pythagoras' Theorem in triangle BCD to find the length of side BC. (ii) Using your answer to part (a)(i), find the area of the top of the cuboid. (iii) Find the volume of the cuboid. (iv) If the volume of the prism is equal to the volume of the cuboid, find the height h of the prism, showing your working at each stage. (v) Find the surface area of the prism.

Answer 1

Please see attached solution
o Ina B CD BP²= BC + co2 (32)² = BC² + (12) 2 1024 = Bc²+144 Bc²= 1024-164 Bc2= 880 Bc²=880cm? BC= √880 cm - J2x2x2x2x55 ВС. Ч m) (6 Area of the top of the cuboicle = exb = 12cm x 4555 cm = 48558 cm2

CD volume of cuboido = exbth - 45cm x 12cm x 12cm = 4X144 555 cm] z 576 555 cm? Area of Bale x height Volume of Prism = volume of Prisma volume of Cuboj de = 576585 com 96 cm xh 576 155 cm3 = 576555 m3 = 6555 cm 96cm2

surface area of prison - Perimeter xheight tax Area of bere of bare = 48cm x 6555umtax 96 = 28 8 555 cm + 14.2 come = 96/3155+2) cm² Please like it