Composite Volumes

1) A cylinder (radius 5 cm, height 10 cm) is attached to a cube with a side length of 10 cm. Find the approximate total volume.

1285 cm³

1785 cm³

2000 cm³

2142 cm³

Volume = (cube) 10×10×10 + (cylinder) 3.14×5×5×10 = 1000 + 785 = 1785 cm³

Explanation

Volume = (cube) 10×10×10 + (cylinder) 3.14×5×5×10 = 1000 + 785 = 1785 cm³

2) A rectangular prism measures 8 cm × 6 cm × 4 cm. A triangular prism with base 8 cm × 4 cm and height 3 cm is placed on top. Find the total volume of the figure.

240 cm³

264 cm³

288 cm³

312 cm³

Volume = (rect prism) 8×6×4 + (tri prism) 0.5×8×4×3 = 192 + 48 = 240 cm³

Explanation

Volume = (rect prism) 8×6×4 + (tri prism) 0.5×8×4×3 = 192 + 48 = 240 cm³

3) A cone (radius 3 cm, height 6 cm) is placed on top of a cylinder (radius 3 cm, height 8 cm). Find the total volume.

113.1 cm³

226.2 cm³

282.7 cm³

339.3 cm³

Volume = (cyl) 3.14×3×3×8 + (cone) 1/3×3.14×3×3×6 = 226.2 + 56.5 = 282.7 cm³

Explanation

Volume = (cyl) 3.14×3×3×8 + (cone) 1/3×3.14×3×3×6 = 226.2 + 56.5 = 282.7 cm³

4) A rectangular prism measures 10 cm × 8 cm × 6 cm. A half-cylinder with radius 4 cm and length 8 cm is attached to the top. Find the approximate total volume.

482 cm³

583 cm³

645 cm³

681 cm³

Volume = (rect prism) 10×8×6 + (half cyl) 0.5×3.14×4×4×8 = 480 + 201 = 681 cm³

Explanation

Volume = (rect prism) 10×8×6 + (half cyl) 0.5×3.14×4×4×8 = 480 + 201 = 681 cm³

5) A sphere of radius 5 cm is cut in half. Find the volume of one half.

261.8 cm³

314.2 cm³

785.4 cm³

523.6 cm³

Volume = 0.5×(4/3×3.14×5×5×5) = 261.8 cm³

Explanation

Volume = 0.5×(4/3×3.14×5×5×5) = 261.8 cm³

6) A cylinder with radius 4 m and height 10 m is attached to a rectangular prism that measures 8 m × 8 m × 4 m, sharing their 8 × 8 base. What is the approximate total volume of the composite solid?

652 m³

702 m³

759 m³

912 m³

Volume = (rect prism) 8×8×4 + (cyl) 3.14×4×4×10 = 256 + 503 = 759 m³

Explanation

Volume = (rect prism) 8×8×4 + (cyl) 3.14×4×4×10 = 256 + 503 = 759 m³

7) A pyramid of height 9 cm sits on top of a cube with a side length of 6 cm. Find the total volume.

324 cm³

288 cm³

274 cm³

360 cm³

Volume = (cube) 6×6×6 + (pyramid) 1/3×6×6×9 = 216 + 108 = 324 cm³

Explanation

Volume = (cube) 6×6×6 + (pyramid) 1/3×6×6×9 = 216 + 108 = 324 cm³

8) A silo is shaped like a cylinder (radius 4 m, height 10 m) with a hemisphere of radius 4 m on top. Find the approximate total volume.

502.7 m³

636.7 m³

804.2 m³

1005.3 m³

Volume = (cyl) 3.14×4×4×10 + (hemisphere) 0.5×4/3×3.14×4×4×4 = 502.7 + 134 = 636.7 m³

Explanation

Volume = (cyl) 3.14×4×4×10 + (hemisphere) 0.5×4/3×3.14×4×4×4 = 502.7 + 134 = 636.7 m³

9) A rectangular prism measures 8 cm × 8 cm × 5 cm. On top is a triangular prism roof with base 8 cm × 5 cm and height 4 cm. Find the volume.

320 cm³

380 cm³

400 cm³

480 cm³

Volume = (rect prism) 8×8×5 + (tri prism) 0.5×8×4×5 = 320 + 80 = 400 cm³

Explanation

Volume = (rect prism) 8×8×5 + (tri prism) 0.5×8×4×5 = 320 + 80 = 400 cm³

10) A cone of radius 7 m and height 12 m is placed on top of a cylinder of radius 7 m and height 20 m. Find the approximate total volume.

1012.4 m³

1801.3 m³

2309.5 m³

3694.6 m³

Volume = (cyl) 3.14×7×7×20 + (cone) 1/3×3.14×7×7×12 = 3078.8 + 615.8 = 3694.6 m³

Explanation

Volume = (cyl) 3.14×7×7×20 + (cone) 1/3×3.14×7×7×12 = 3078.8 + 615.8 = 3694.6 m³

11) A water tank is shaped like a rectangular prism (6 × 6 × 12) with a half cylinder of radius 3, length 6 on top. Find the approximate volume.

400 cm³

432 cm³

504 cm³

517 cm³

Volume = (rect prism) 6×6×12 + (half cyl) 0.5×3.14×3×3×6 = 432 + 84.8 = 517 cm³

Explanation

Volume = (rect prism) 6×6×12 + (half cyl) 0.5×3.14×3×3×6 = 432 + 84.8 = 517 cm³

12) A cube has side length 8 cm. On top of it sits a square pyramid with base 8 cm × 8 cm and height 6 cm. Find the total volume.

320 cm³

484 cm³

525 cm³

640 cm³

Volume = (cube) 8×8×8 + (pyramid) 1/3×8×8×6 = 512 + 128 = 640 cm³

Explanation

Volume = (cube) 8×8×8 + (pyramid) 1/3×8×8×6 = 512 + 128 = 640 cm³

13) A hemisphere of radius 6 cm is placed on top of a cylinder of radius 6 cm and height 10 cm. Find the total volume.

904.8 cm³

1130.9 cm³

1583.4 cm³

1727.9 cm³

Volume = (cyl) 3.14×6×6×10 + (hemisphere) 0.5×4/3×3.14×6×6×6 = 1131 + 452.4 = 1583.4 cm³

Explanation

Volume = (cyl) 3.14×6×6×10 + (hemisphere) 0.5×4/3×3.14×6×6×6 = 1131 + 452.4 = 1583.4 cm³

14) A cube of side 4 cm has a cylinder (radius 2 cm, height 4 cm) removed from it. Find the approximate remaining volume.

13.7 cm³

21.2 cm³

24.3 cm³

28.4 cm³

Volume = (cube) 4×4×4 - (cyl) 3.14×2×2×4 = 64 - 50.3 = 13.7 cm³

Explanation

Volume = (cube) 4×4×4 - (cyl) 3.14×2×2×4 = 64 - 50.3 = 13.7 cm³

15) A rectangular prism measures 20 cm × 10 cm × 5 cm. A quarter cylinder with radius 5 cm and height 10 cm is attached to the side. Find the approximate total volume.

1034.1 cm³

1078.5 cm³

1196.3 cm³

1550.1 cm³

Volume = (rect prism) 20×10×5 + (quarter cyl) 0.25×3.14×5×5×10 = 1000 + 196.3 = 1196.3 cm³

Explanation

Volume = (rect prism) 20×10×5 + (quarter cyl) 0.25×3.14×5×5×10 = 1000 + 196.3 = 1196.3 cm³

16) A cube has a side length of 12 cm. A hemisphere with radius 6 cm is placed on top of the cube. Find the approximate total volume of the solid.

2180 cm³

2232 cm³

2592 cm³

2670 cm³

Volume = (cube) 12×12×12 + (hemisphere) 0.5×4/3×3.14×6×6×6 = 1728 + 452.4 = 2180 cm³

Explanation

Volume = (cube) 12×12×12 + (hemisphere) 0.5×4/3×3.14×6×6×6 = 1728 + 452.4 = 2180 cm³

17) A rectangular prism measures 10 cm × 8 cm × 4 cm. A hemisphere with radius 4 cm is attached on top. Find the approximate total volume.

420 cm³

454 cm³

534 cm³

610 cm³

Volume = (rect prism) 10×8×4 + (hemisphere) 0.5×4/3×3.14×4×4×4 = 320 + 134 = 454 cm³

Explanation

Volume = (rect prism) 10×8×4 + (hemisphere) 0.5×4/3×3.14×4×4×4 = 320 + 134 = 454 cm³

18) A triangular prism of base 12 cm and height 8 cm, length 10 cm, is attached to a cube of side 10 cm. Find the total volume.

1480 cm³

1560 cm³

1680 cm³

1760 cm³

Volume = (cube) 10×10×10 + (tri prism) 0.5×12×8×10 = 1000 + 480 = 1480 cm³

Explanation

Volume = (cube) 10×10×10 + (tri prism) 0.5×12×8×10 = 1000 + 480 = 1480 cm³

19) A dome-shaped observatory consists of a cylinder with radius 10 m and height 15 m, topped by a hemisphere of radius 10 m. Find the approximate total volume.

4712 m³

6806 m³

7854 m³

9425 m³

Volume = (cyl) 3.14×10×10×15 + (hemisphere) 0.5×4/3×3.14×10×10×10 = 4712.4 + 2094.4 = 6806 m³

Explanation

Volume = (cyl) 3.14×10×10×15 + (hemisphere) 0.5×4/3×3.14×10×10×10 = 4712.4 + 2094.4 = 6806 m³