To find the volume of each figure, we use the formula for the volume of a pyramid or cone:
Volume = (1/3) × Base Area × Height
We’ll go through each problem one by one. All answers are rounded to the nearest tenth if needed.
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1) Triangular base: base = 8 yd, height of triangle = 7 yd → Area = (1/2)(8)(7) = 28 yd²
Pyramid height = 10 yd
Volume = (1/3)(28)(10) = 280/3 ≈
93.3 yd³
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2) Circular base: radius = 1 ft → Area = π(1)² = π ft²
Cone height = 7 ft
Volume = (1/3)(π)(7) ≈ (1/3)(3.1416)(7) ≈ 7.330 ≈
7.3 ft³
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3) Rectangular base: 2 mi × 3 mi = 6 mi²
Pyramid height = 4 mi
Volume = (1/3)(6)(4) = 24/3 =
8.0 mi³
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4) Square base: 9 cm × 9 cm = 81 cm²
Pyramid height = 11 cm
Volume = (1/3)(81)(11) = 891/3 =
297.0 cm³
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5) Rectangular base: 8 cm × 3 cm = 24 cm²
Pyramid height = 7 cm
Volume = (1/3)(24)(7) = 168/3 =
56.0 cm³
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6) Triangular base: base = 11 km, height of triangle = 9 km → Area = (1/2)(11)(9) = 49.5 km²
Pyramid height = 11 km
Volume = (1/3)(49.5)(11) = 544.5 / 3 =
181.5 km³
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7) Rectangular base: 10 m × 5 m = 50 m²
Pyramid height = 9 m
Volume = (1/3)(50)(9) = 450/3 =
150.0 m³
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8) Rectangular base: 2 mi × 1 mi = 2 mi²
Pyramid height = 2 mi
Volume = (1/3)(2)(2) = 4/3 ≈
1.3 mi³
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9) Square base: 6 ft × 6 ft = 36 ft²
Pyramid height = 6 ft
Volume = (1/3)(36)(6) = 216/3 =
72.0 ft³
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10) Circular base: radius = 6 yd → Area = π(6)² = 36π yd²
Cone height = 12 yd
Volume = (1/3)(36π)(12) = 144π ≈ 144 × 3.1416 ≈ 452.389 ≈
452.4 yd³
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11) Rectangular base: 6 ft × 3 ft = 18 ft²
Pyramid height = 6 ft
Volume = (1/3)(18)(6) = 108/3 =
36.0 ft³
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12) Square base: 5 mi × 5 mi = 25 mi²
Pyramid height = 6 mi
Volume = (1/3)(25)(6) = 150/3 =
50.0 mi³
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Final Answer:
1) 93.3
2) 7.3
3) 8.0
4) 297.0
5) 56.0
6) 181.5
7) 150.0
8) 1.3
9) 72.0
10) 452.4
11) 36.0
12) 50.0
Parent Tip: Review the logic above to help your child master the concept of kuta worksheet geometry.
