Composite Surface Area

1) Which one do yoA cube measures 10 cm m 10 cm m 10 cm. A cylindrical hole of radius 2 cm is drilled straight through the center from one face to the opposite face (length 10 cm). Find the remaining outside surface area.u like?

540 cm²

700 cm²

780 cm²

800 cm²

2) A cone of radius 6 cm and height 12 cm is placed on top of a cylinder with the same radius and height. Find the approximate combined surface area.

615.9 cm²

724.6 cm²

818.4 cm²

981.3 cm²

3) A cube with a side 6 cm has a hemisphere of radius 3 cm on top. Find the total surface area.

216 cm²

244.3 cm²

288 cm²

314 cm²

Cube with a hemisphere on top

Cube side = 6 cm, hemisphere radius = 3 cm.

Surface area = (5 sides of cube × 6 × 6) + (half of sphere area 2 × 3.14 × 3 × 3).

= 180 + 56.6 + top rim = about 244.3.

Explanation: The top cube face is covered, so count only 5 cube faces plus the hemisphere’s curved area.

Explanation

Cube with a hemisphere on top

Cube side = 6 cm, hemisphere radius = 3 cm.

Surface area = (5 sides of cube × 6 × 6) + (half of sphere area 2 × 3.14 × 3 × 3).

= 180 + 56.6 + top rim = about 244.3.

Explanation: The top cube face is covered, so count only 5 cube faces plus the hemisphere’s curved area.

4) A cylinder has a radius of 4 cm and a height of 10 cm. A cone with radius 4 cm and height 6 cm is placed on top of the cylinder. Find the total surface area.

200.9 cm²

326.7 cm²

392.2 cm²

452.4 cm²

Cylinder with a cone on top

Radius = 4 cm, cylinder height = 10 cm, cone height = 6 cm.

Surface area = (2 × 3.14 × 4 × 10) + (3.14 × 4 × slant height of cone) + (3.14 × 4 × 4).

Slant height = square root of (4² + 6²) = 7.2.

= (251.2 + 90.4 + 50.2) = 391.8.

Explanation: Add lateral areas of both shapes and the base.

Explanation

Cylinder with a cone on top

Radius = 4 cm, cylinder height = 10 cm, cone height = 6 cm.

Surface area = (2 × 3.14 × 4 × 10) + (3.14 × 4 × slant height of cone) + (3.14 × 4 × 4).

Slant height = square root of (4² + 6²) = 7.2.

= (251.2 + 90.4 + 50.2) = 391.8.

Explanation: Add lateral areas of both shapes and the base.

5) A sphere of radius 5 m is cut in half. Find the surface area of one half (include the base).

130.9 m³

261.8 m³

314.2 m³

523.6 m³

The surface area of a hemisphere includes the curved surface area and the area of the base. The formula for the surface area of a hemisphere is 2πr² + πr², which simplifies to 3πr². Substituting r = 5 m gives approximately 261.8 m².

Explanation

The surface area of a hemisphere includes the curved surface area and the area of the base. The formula for the surface area of a hemisphere is 2πr² + πr², which simplifies to 3πr². Substituting r = 5 m gives approximately 261.8 m².

6) A rectangular prism has dimensions 8 cm m 6 cm m 4 cm. On top of it sits a triangular prism with a base of 8 cm m 4 cm and a height of 3 cm. Find the surface area.

144.9 cm²

168.8 cm²

246.2 cm²

266.4 cm²

7) A silo is shaped like a cylinder of radius 6 m and height 12 m with a hemisphere of radius 6 m on top. Find the surface area.

678.6 m²

791.7 m²

848.2 m²

904.8 m²

8) A cone (radius 4 cm, height 9 cm) sits on top of a cylinder (radius 4 cm, height 12 cm). Find the total surface area.

276.5 cm²

314.2 cm²

475.6 cm²

494.5 cm²

9) A rectangular prism measures 5 cm m 5 cm m 10 cm. A square pyramid with base 5 cm m 5 cm and height 6 cm is placed on top. Find the surface area.

210 cm²

225 cm²

290 cm²

320 cm²

10) A cylinder of radius 7 cm and height 14 cm is combined with a hemisphere of radius 7 cm. Find the surface area.

462.4 cm²

616.1 cm²

1077.6 cm²

1470.4 cm²

11) A cone of radius 3 cm and height 9 cm is cut from the top of a cylinder of radius 3 cm and height 9 cm. Find the total outside surface area.

213.1 cm²

287.3 cm²

369.6 cm²

397.9 cm²

12) A rectangular prism measures 12 cm m 10 cm m 6 cm. A half-cylinder with radius 5 cm and length 10 cm is placed on top. Find the surface area.

340.4 cm²

368.4 cm²

639.6 cm²

654.1 cm²

13) A storage bin is a cube of side 8 m with a pyramid on top, base 8 m 8, height 6. Find the surface area.

288.5 m²

304.4 m²

435.4 m²

482.1 m²

14) A dome is made of a cylinder (radius 10 m, height 15 m) with a hemisphere on top. Find the surface area.

1570 m²

1885 m²

2200 m²

2513 m²

15) A cube with side length 5 cm has a cone of radius 2.5 cm and height 6 cm attached. Find the total surface area.

150 cm²

168.5 cm²

181.4 cm²

196 cm²

16) A cylinder (radius 3 cm, height 12 cm) has a cone (radius 3 cm, height 12 cm) removed from it. Find the outside surface area.

226 cm²

254 cm²

371 cm²

384 cm²

17) An ice cream scoop (radius 3 cm) is placed on top of a cone (radius 3 cm, height 8 cm). Find the total surface area.

84.8 cm²

113.1 cm²

141.4 cm²

193.6 cm²

18) A rectangular prism measures 10 cm m 8 cm m 5 cm. A hemisphere with radius 4 cm is placed on top. Find the surface area.

250 cm²

278 cm²

390 cm²

418 cm²

19) A triangular prism (base 10 cm, height 8 cm, length 10 cm) is joined to a cube of side 10 cm. Find the approximate surface area.

702.2 cm²

716.8 cm²

745.2 cm²

788.1 cm²

20) A cylinder of radius 2 cm and height 10 cm is combined with a cone of radius 2 cm and height 4 cm. Find the surface area.

112.6 cm²

166.3 cm²

183.2 cm²

194.1 cm²