Question

Find the volume of the following shapes. Round to tenths and don’t forget the units. Show your work!

Answer 1

Answer:

Step-by-step explanation:

1). Figure (1) comprises two cuboids, one small cuboid placed on the big cuboid at the bottom.

Volume of the figure = Volume of the cuboid on the top + Volume of the cuboid at the bottom

Volume of the cuboid on the top = Length × Width × Height

                                                   = 4 × 6 × 5

                                                   = 120 mm³

Volume of the cuboid at the bottom = Length × Width × Height

                                                        = 9 × 6 × 4

                                                        = 216 mm³

Volume of the figure = 120 + 216

                                   = 336 mm³

2). Figure shown in the picture has two parts,

Cone placed on the top of a cylinder.

Volume of the given figure = Volume of cone + Volume of cylinder

                                          = $\frac{1}{3}\pi r^{2}h+\pi r^{2}h'$

                                          = $\frac{1}{3}\pi (\frac{3}{2})^{2}(3)+\pi (\frac{3}{2})^{2}(8.1)$

                                          = $\frac{9}{4}\pi +18.225\pi$

                                          = $(2.25+18.225)\pi$

                                          = $20.475\pi$

                                          = 64.3 ft³

Therefore, volume of the given figure = 64.3 ft³.