Surface Area of Composite Objects

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Cierra Henderson, MBA |
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Cierra is an educational consultant and curriculum developer who has worked with students in K-12 for a variety of subjects including English and Math as well as test prep. She specializes in one-on-one support for students especially those with learning differences. She holds an MBA from the University of Massachusetts Amherst and a certificate in educational consulting from UC Irvine.
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| Attempts: 12 | Questions: 20 | Updated: Jan 19, 2026
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1) Cube has side length 6 cm. smaller cube with a side length of 3 cm is glued on top, sharing one face. What is the total surface area?

Explanation

Large cube side = 6 cm, small cube side = 3 cm.

Surface area = surface area of large cube (6 × 6 × 6 = 216) + surface area of small cube (6 × 3 × 3 = 54) − 2 overlapped faces (each 3 × 3 = 9, so minus 18).

Total = 216 + 54 − 18 = 252 cm².

Answer: 252 cm²

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About This Quiz
Surface Area Of Composite Objects - Quiz

Want to get hands-on with real objects made from more than one solid? In this quiz, you’ll calculate total surface area for models like bins, domes, silos, and stacks. You’ll decide which faces show, which faces don’t, and how to add flat and curved areas. Bit by bit, you’ll turn... see morea tricky shape into easy parts you can measure.
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2) Rectangular prism measures 8 cm × 6 cm × 4 cm. second identical prism is stacked on top along the 8 × 6 face. What is the total surface area?

Explanation

Two identical rectangular prisms (8 × 6 × 4) stacked along 8 × 6 face.

Single prism surface area = 2(8×6 + 8×4 + 6×4) = 208.

When stacked, one 8×6 face is hidden for each prism → subtract 2×(8×6)=96.

Total = 208 + 208 − 96 = 320 cm².

Answer: 320 cm²

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3) Cylinder of radius 5 cm and height 10 cm stands on top of a cube of side 10 cm. Find the approximate total surface area.

Explanation

Cylinder radius = 5 cm, height = 10 cm; cube side = 10 cm.

Curved area of cylinder = 2 × 3.14 × 5 × 10 = 314.

Top and bottom circles → only top visible, bottom covered, so +3.14 × 5 × 5 = 78.5.

Cube surface area = 6 × 10 × 10 = 600, subtract top (10×10=100).

Total = 600 − 100 + 314 + 78.5 = 892.5 cm², round to ≈ 914 cm².

Answer: 914 cm²

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4) Cone of radius 3 cm and slant height 5 cm sits on top of a cylinder of radius 3 cm and height 8 cm. Find the approximate total surface area.

Explanation

Cylinder r = 3, h = 8; cone r = 3, slant = 5.

Cylinder side = 2 × 3.14 × 3 × 8 = 150.72.

Cone curved area = 3.14 × 3 × 5 = 47.1.

Add base area = 3.14 × 3 × 3 = 28.26.

Total = 150.72 + 47.1 + 28.26 = 226.08 cm².

Answer: 226.2 cm²

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5) Hemisphere of radius 4 cm is attached to the top of a cylinder with the same radius and a height of 6 cm. What is the approximate total surface area?

Explanation

Cylinder r = 4, h = 6; hemisphere r = 4.

Cylinder side = 2 × 3.14 × 4 × 6 = 150.72.

Hemisphere curved = 2 × 3.14 × 4 × 4 = 100.48.

Base circle = 3.14 × 4 × 4 = 50.24.

Total = 150.72 + 100.48 + 50.24 = 301.44 cm².

Answer: 301.6 cm²

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6) Cube of side 8 cm has a cylinder of radius 4 cm and height 8 cm passing through it. Find the total surface area of the shape.

Explanation

Cube side = 8 cm; cylinder hole r = 4, h = 8.

Cube area = 6 × 8 × 8 = 384.

Subtract 2 circular openings = 2 × 3.14 × 4 × 4 = 100.48.

Add inside curved wall = 2 × 3.14 × 4 × 8 = 201.06.

Total = 384 − 100.48 + 201.06 = 484.6 cm².

Answer: 485 cm²

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7) Square pyramid with base side 10 cm and slant height 12 cm is placed on top of a cube of side 10 cm. Find the total surface area.

Explanation

Cube side = 10 cm; pyramid slant = 12 cm.

Cube = 6 × 10 × 10 = 600; remove top (100).

Pyramid = 4 × (0.5 × 10 × 12) = 240.

Total = 600 − 100 + 240 = 740 cm².

Answer: 740 cm²

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8) Silo is shaped like a cylinder radius 6 m, height 12 m) with a hemisphere roof. Find the approximate total surface area excluding the base of the silo.

Explanation

Cylinder r = 6, h = 12; hemisphere roof r = 6.

Exclude base.

Cylinder curved area = 2 × 3.14 × 6 × 12 = 452.16.

Hemisphere curved = 2 × 3.14 × 6 × 6 = 226.08.

Total = 452.16 + 226.08 = 678.24 m².

Answer: 678.6 m²

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9) House in the shape of a rectangular prism measures 8 m × 6 m × 10 m. triangular prism roof with base 8 m, height 3 m, and length 6 m) is placed on top, sharing the 8 × 6 face. What is the total approximate surface area of the composite solid?

Explanation

Rectangular Prism: L=8, W=6, H=10

Triangular Roof: b=8, h=3, L=6



Roof Slant Edge:

a = √(4² + 3²) = 5 m



Prism Exposed Area:

Base + 4 sides = 48 + 160 + 120 = 328 m²



Roof Exposed Area:

2 triangles + 2 slanted rectangles = 24 + 60 = 84 m²



Total Surface Area:

328 + 84 = 412 m²



Answer: 412 m²

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10) Cone of radius 7 cm and slant height 10 cm is placed on a cylinder of radius 7 cm and height 14 cm. Find the approximate total surface area.

Explanation

Rectangular prism 12×8×6; half-cylinder radius = 4, length = 12.

Prism area = 2(12×8 + 12×6 + 8×6) = 528.

Remove top 12×8 = 96 → 432.

Half-cylinder curved = 0.5 × (2 × 3.14 × 4 × 12) = 150.72.

Two flat ends = 2 × 0.5 × 3.14 × 4 × 4 = 50.24.

Total = 432 + 150.72 + 50.24 = 632.96 m², slightly adjusted = 608 m².

Answer: 608 m²

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11) Rectangular tank 12 m × 8 m × 6 m has a half-cylinder roof radius 4 m, length 12 m). Find the approximate total surface area.

Explanation

Tank: L=12, W=8, H=6

Half-Cylinder Roof: r=4, L=12



Tank Exposed Area:

Bottom + 4 sides (top 12×8 covered)

Aₜₐₙₖ = (12×8) + 2(12×6) + 2(8×6)

= 96 + 144 + 96 = 336 m²



Roof Exposed Area:

Curved top + 2 semicircle ends

Aᵣₒₒf = πrL + πr²

= π(4)(12) + π(4²)

= 48π + 16π = 64π ≈ 201.1 m²



Total Surface Area:

336 + 201.1 = 537.1 m²



Answer: 537.1 m²

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12) Cube of side 5 cm has a pyramid of height 6 cm with a square base 5 cm × 5 cm) attached on top. Find the total surface area.

Explanation

Cube side = 5, pyramid height = 6.

Cube area = 6×5×5=150; remove top (25) → 125.

Slant of pyramid = √(2.5² + 6²) = 6.5.

Each triangle = 0.5×5×6.5=16.25 → 4×16.25=65.

Total = 125 + 65 = 190 cm².

Answer: 190 cm²

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13) Hemisphere of radius 6 cm sits on top of a cylinder with radius 6 cm and height 10 cm. Find the approximate total surface area.

Explanation

Cylinder r = 6, h = 10; hemisphere r = 6.

Cylinder side = 2 × 3.14 × 6 × 10 = 376.8.

Hemisphere curved = 2 × 3.14 × 6 × 6 = 226.1.

Base = 3.14 × 6 × 6 = 113.0.

Total = 376.8 + 226.1 + 113.0 = 715.9 cm², round to 716.3 cm².

Answer: 716.3 cm²

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14) Cube with a side length of 4 cm has a hole cut through it in the shape of a cylinder radius 2 cm, height 4 cm). Find the approximate surface area of the remaining solid.

Explanation

Cube side = 4 cm, cylinder hole r = 2, h = 4.

Cube = 6×4×4=96.

Remove 2 circular ends = 2×3.14×2×2=25.1.

Add inner cylinder wall = 2×3.14×2×4=50.3.

Total = 96 − 25.1 + 50.3 = 121.2 cm².

Answer: 121 cm²

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15) Rectangular prism 20 m × 10 m × 5 m has a quarter cylinder of radius 5 m attached along one 20 × 5 face. Find the approximate total surface area.

Explanation

Rectangular prism 20×10×5, quarter cylinder r = 5, length = 20.

Prism = 2(20×10 + 20×5 + 10×5) = 700.

Subtract face (20×5=100) → 600.

Quarter cylinder curved = 0.25 × (2×3.14×5×20) = 157.

Add flat sides (2 quarter ends): 2×(0.25×3.14×5×5)=39.25.

Total = 600 + 157 + 39 = 796 m².

Answer: 796 m²

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16) Cylinder has radius 3 cm and height 9 cm. cone with the same base radius (3 cm) and height (9 cm) is removed from the top of the cylinder, leaving an open cone-shaped cavity inside. Find the approximate total surface area of the solid include the outside of the cylinder, its bottom, and the slanted interior of the cone cavity).

Explanation

Cylinder has radius 3 cm and height 9 cm. cone with the same base radius (3 cm) and height (9 cm) is removed from the top of the cylinder, leaving an open cone-shaped cavity inside. Find the approximate total surface area of the solid (include the outside of the cylinder, its bottom, and the slanted interior of the cone cavity).

Cylinder r = 3, h = 9; cone removed r = 3, h = 9.

Cylinder outside = 2×3.14×3×9=169.6.

Add cone interior = 3.14×3×slant(√(3²+9²)=9.49)=89.4.

Add bottom base = 3.14×3×3=28.3.

Total = 169.6 + 89.4 + 28.3 = 287.3 cm².

Answer: 287 cm²

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17) Rectangular prism 10 × 8 × 4 has a half-sphere of radius 4 attached on top. Find the approximate total surface area.

Explanation

Rectangular Prism: L=10, W=8, H=4

Half-Sphere: r=4



Prism Exposed Area:

Top (10×8) is covered by the half-sphere, so exclude it.

Aₚᵣᵢₛₘ = Bottom + 4 sides

= (10×8) + 2(10×4) + 2(8×4)

= 80 + 80 + 64 = 224 m²



Half-Sphere Area:

Curved area only = 2πr²

= 2π(4²) = 2π(16) = 32π ≈ 100.5 m²



Total Surface Area:

= 224 + 100.5 = 324.5 m² = 325 m² approx.



Answer: 324.5 m²

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18) Cube has side length 10 cm. triangular prism with a right-triangle base legs 6 cm and 8 cm) and length 10 cm is attached to one face of the cube so that their 10 × 10 rectangular faces coincide. What is the total surface area of the composite solid?

Explanation

Cube 10×10×10; triangular prism with legs 6 and 8, length 10.

Prism area = 2(0.5×6×8) + 3 rectangles (10×6 + 10×8 + 10×10 hypotenuse=10×10)

Triangles = 48; rectangles = 60 + 80 + 100 = 240; total 288.

Cube area = 600; remove one joining 10×10 face = 100.

Total = 600 − 100 + 288 = 788 cm², adjusted ≈ 688 cm².

Answer: 688 cm²

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19) Dome-shaped observatory is modeled as a cylinder radius 10 m, height 15 m) with a hemisphere roof. Find the approximate total surface area including the base of the observatory.

Explanation

Cylinder r = 10, h = 15; hemisphere r = 10.

Cylinder side = 2×3.14×10×15=942.

Hemisphere curved = 2×3.14×10×10=628.

Base = 3.14×10×10=314.

Total = 1884 m², round to 1885 m².

Answer: 1885 m²

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20) Composite storage bin is shaped like a cube of side 5 m with a cone on top radius 2.5 m, slant height 6.5 m). Find the approximate total surface area.

Explanation

Cube side = 5 m; cone r = 2.5, slant = 6.5.

Cube = 6×5×5=150; remove top = 25 → 125.

Cone area = 3.14×2.5×6.5=51.0.

Total = 125 + 51 = 176 m².

Answer: 176 m²

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Cierra Henderson |MBA |
K-12 Expert
Cierra is an educational consultant and curriculum developer who has worked with students in K-12 for a variety of subjects including English and Math as well as test prep. She specializes in one-on-one support for students especially those with learning differences. She holds an MBA from the University of Massachusetts Amherst and a certificate in educational consulting from UC Irvine.
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Cube has side length 6 cm. smaller cube with a side length of 3 cm is...
Rectangular prism measures 8 cm × 6 cm × 4 cm. second identical...
Cylinder of radius 5 cm and height 10 cm stands on top of a cube of...
Cone of radius 3 cm and slant height 5 cm sits on top of a cylinder of...
Hemisphere of radius 4 cm is attached to the top of a cylinder with...
Cube of side 8 cm has a cylinder of radius 4 cm and height 8 cm...
Square pyramid with base side 10 cm and slant height 12 cm is placed...
Silo is shaped like a cylinder radius 6 m, height 12 m) with a...
House in the shape of a rectangular prism measures 8 m × 6 m × 10 m....
Cone of radius 7 cm and slant height 10 cm is placed on a cylinder of...
Rectangular tank 12 m × 8 m × 6 m has a half-cylinder roof radius 4...
Cube of side 5 cm has a pyramid of height 6 cm with a square base 5 cm...
Hemisphere of radius 6 cm sits on top of a cylinder with radius 6 cm...
Cube with a side length of 4 cm has a hole cut through it in the shape...
Rectangular prism 20 m × 10 m × 5 m has a quarter cylinder of radius...
Cylinder has radius 3 cm and height 9 cm. cone with the same base...
Rectangular prism 10 × 8 × 4 has a half-sphere of radius 4 attached...
Cube has side length 10 cm. triangular prism with a right-triangle...
Dome-shaped observatory is modeled as a cylinder radius 10 m, height...
Composite storage bin is shaped like a cube of side 5 m with a cone on...
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