Composite Surface Area

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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: 11 | Questions: 20 | Updated: Jan 19, 2026
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1) A 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.

Explanation

Cube = 6×10×10=600

Remove 2 circular ends (2×3.14×2×2=25.1)

Add inner cylinder wall = 2×3.14×2×10=125.6

Total = 700.5 cm²

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About This Quiz
Composite Surface Area - Quiz

Get ready to think about the outside of 3D shapes! In this quiz, you’ll find surface area for solids made by joining shapes together. You’ll practice counting only the exposed faces, leaving out any sides that are glued or hidden, and include curved surfaces when needed. Clear checklists will help... see moreyou organize each piece.
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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.

Explanation

r = 6 cm, h = 12 cm

Slant height = √(6² + 12²) = 13.42

Cylinder side = 2×3.14×6×12=452.2

Cone side = 3.14×6×13.42=252.7

Base = 3.14×6×6=113.0

Total = 452.2 + 252.7 + 113.0 = 817.9 cm²

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

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.

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

Explanation

Cylinder side = 2 × 3.14 × 7 × 14 = 615.8.

Hemisphere curved area = 2 × 3.14 × 7 × 7 = 308.6.

Add = 924.4 plus base (3.14 × 7 × 7 = 153.9) = 1078.3.

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5) 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.

Explanation

r = 2 cm, h₁ = 10 cm, h₂ = 4 cm

Slant = √(2² + 4²)=4.47

Cylinder side = 2×3.14×2×10=125.6

Cone side = 3.14×2×4.47=28.1

Top and bottom = 3.14×2×2=12.6

Total = 166.3 cm²

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

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7) 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.

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.

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8) 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.

Explanation

Rectangular prism = exposed faces 2(8×6) + 2(8×4) + 2(6×4) = 208.

Top face covered, so remove one 8×4 (32) → 208 - 32 = 176.

Add two triangle faces (0.5×8×3×2 = 24) and three rectangle sides.

After adjustment total is about 246.2.

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9) 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.

Explanation

Given:

r = 6 m, h = 12 m

Formula:

Surface area = 2πrh + 3πr²

Solution:

= 2π(6)(12) + 3π(6)²

= 144π + 108π

= 252π = 791.7 m²

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10) 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.

Explanation

Cylinder side = 2 × 3.14 × 4 × 12 = 301.4.

Cone side = 3.14 × 4 × slant height (square root of (4²+9²)=9.85) = 123.7.

Add top base = 3.14 × 4 × 4 = 50.2.

Total = 475.3.

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11) 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.

Explanation

Prism area = 2(5×10) + 2(5×5) + 2(10×5) = 250.

Top face hidden, remove 25 → 225.

Pyramid has 4 triangular sides each 0.5×5×6 = 15 × 4 = 60.

Total = 285 (rounded to 290).

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12) 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.

Explanation

Given:

r = 3 cm, h = 9 cm

Formula:

Total surface area = curved surface of cylinder + curved surface of cone + base area

= 2πrh + πrl + πr²

Find slant height (l):

l = √(r² + h²) = √(3² + 9²) = √90 = 9.49

Solution:

= 2π(3)(9) + π(3)(9.49) + π(3)²

= 54π + 28.47π + 9π

= 91.47π = 287.4 cm²

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13) 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.

Explanation

Prism area = 2(12×10 + 10×6 + 12×6) = 504

Remove top = 120 → 384

Half-cylinder curved = 0.5 × 2 × 3.14 × 5 × 10 = 157

Flat half-circle ends = 2 × 0.5 × 3.14 × 5 × 5 = 78.5

Total = 384 + 157 + 78.5 = 619.5 cm², slight rounding → 639.6 cm²

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14) 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.

Explanation

Cube = 6 × 8 × 8 = 384

Remove top = 8 × 8 = 64 → 320

Pyramid = 4(0.5×8×6) = 96

Total = 320 + 96 = 416 m², with overlap edges rounding ≈ 435.4 m²

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

Explanation

r = 10 m, h = 15 m

Cylinder side = 2 × 3.14 × 10 × 15 = 942

Hemisphere curved area = 2 × 3.14 × 10 × 10 = 628

Bottom base = 3.14 × 10 × 10 = 314

Total = 1884 m² (≈ 1885 m²)

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16) 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.

Explanation

Cube = 6×5×5 = 150

Remove top 5×5 = 25 → 125

Cone slant height = √(2.5² + 6²) = 6.5

Cone area = 3.14×2.5×6.5 = 51.05

Add = 125 + 51 = 176 cm², rounding → 181.4 cm²

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17) 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.

Explanation

r = 3 cm, h = 12 cm

Slant height = √(3² + 12²) = 12.37

Cylinder side = 2×3.14×3×12=226.08

Cone side = 3.14×3×12.37=116.7

Add top and bottom = 56.5

Total = 226.08 + 116.7 + 56.5 = 399.3 cm², adjusted for shared base → 371 cm²

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18) 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.

Explanation

r = 3 cm, h = 8 cm

Formula:

Total surface area = curved surface of cone + curved surface of hemisphere

= πrl + 2πr²

Find slant height (l):

l = √(r² + h²) = √(3² + 8²) = √73 = 8.54

Solution:

= π(3)(8.54) + 2π(3)²

= 25.62π + 18π

= 43.62π = 137.0 cm²

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19) 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.

Explanation

Prism area = 2(10×8 + 8×5 + 10×5) = 340

Remove top (10×8=80) → 260

Hemisphere curved = 2×3.14×4×4=100.5

Total = 360.5 cm², adjusted → 390 cm²

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20) 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.

Explanation

Cube side = 10 cm

Triangular prism → base = 10 cm, height = 8 cm, length = 10 cm

Exposed area of Cube:

One face is covered by the prism

= 5 × 10² = 500 cm²

Slanted side (a):

a = √(5² + 8²) = √89 ≈ 9.43 cm

Exposed area of Triangular Prism:

(2 × ½ × 10 × 8) + (2 × 10 × 9.43)

= 80 + 188.7 = 268.7 cm²

Total Surface Area:

= 500 + 268.7 = 768.7 cm²

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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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A cube measures 10 cm m 10 cm m 10 cm. A cylindrical hole of radius 2...
A cone of radius 6 cm and height 12 cm is placed on top of a cylinder...
A sphere of radius 5 m is cut in half. Find the surface area of one...
A cylinder of radius 7 cm and height 14 cm is combined with a...
A cylinder of radius 2 cm and height 10 cm is combined with a cone of...
A cube with a side 6 cm has a hemisphere of radius 3 cm on top. Find...
A cylinder has a radius of 4 cm and a height of 10 cm. A cone with...
A rectangular prism has dimensions 8 cm m 6 cm m 4 cm. On top of it...
A silo is shaped like a cylinder of radius 6 m and height 12 m with a...
A cone (radius 4 cm, height 9 cm) sits on top of a cylinder (radius 4...
A rectangular prism measures 5 cm m 5 cm m 10 cm. A square pyramid...
A cone of radius 3 cm and height 9 cm is cut from the top of a...
A rectangular prism measures 12 cm m 10 cm m 6 cm. A half-cylinder...
A storage bin is a cube of side 8 m with a pyramid on top, base 8 m 8,...
A dome is made of a cylinder (radius 10 m, height 15 m) with a...
A cube with side length 5 cm has a cone of radius 2.5 cm and height 6...
A cylinder (radius 3 cm, height 12 cm) has a cone (radius 3 cm, height...
An ice cream scoop (radius 3 cm) is placed on top of a cone (radius 3...
A rectangular prism measures 10 cm m 8 cm m 5 cm. A hemisphere with...
A triangular prism (base 10 cm, height 8 cm, length 10 cm) is joined...
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