Unit 13 Practice Problems
Unit 13 Practice Problems
Cylinder:
Problem 1:
A cylinder has a radius of 8 cm and a height of 15 cm. Calculate its surface area and volume.
Problem 2:
A cylindrical container has a radius of 5 cm and a height of 12 cm. Find its surface area and volume.
Cone:
Problem 1:
A cone has a radius of 6 cm and a slant height of 10 cm. Determine its surface area and volume.
Problem 2:
A cone-shaped party hat has a radius of 3 cm and a height of 8 cm. Find its surface area and volume.
Pyramid:
Problem 1:
A square pyramid has a base side length of 10 cm and a height of 7 cm. Calculate its surface area and volume.
Problem 2:
A pyramid-shaped chocolate has a square base with sides measuring 6 cm, and a height of 9 cm. Find its surface area and volume.
Sphere:
Problem 1:
A sphere has a radius of 4 cm. Calculate its surface area and volume.
Problem 2:
A ball with a perfectly spherical shape has a radius of 7 cm. Determine its surface area and volume.
Hemisphere (without lid):
Problem 1:
A hemisphere has a radius of 5 cm. Determine its surface area and volume, considering only the curved surface and not the flat base.
Problem 2:
A half-sphere-shaped bowl has a radius of 8 cm. Find its surface area and volume, excluding the flat base.
Hemisphere (with lid):
Problem 1:
A hemisphere, including the flat base, has a radius of 12 cm. Calculate its total surface area and volume.
Problem 2:
A decorative glass ornament is shaped like a hemisphere with a radius of 6 cm, including the flat base. Find its total surface area and volume.
Brahmagupta's Formula (For the Area of a Quadrilateral):
Problem 1:
A quadrilateral has side lengths of 8 cm, 10 cm, 12 cm, and 14 cm. Find its area using Brahmagupta's formula.
Problem 2:
A cyclic quadrilateral has side lengths of 6 cm, 7 cm, 9 cm, and 10 cm. Determine its area using Brahmagupta's formula.
Heron's Formula (For the Area of a Triangle):
Problem 1:
A triangle has side lengths of 5 cm, 7 cm, and 9 cm. Calculate its area using Heron's formula.
Problem 2:
A triangle has side lengths of 12 cm, 16 cm, and 20 cm. Find its area using Heron's formula.
Answers
Cylinder:
Problem 1:
Surface Area = 772π cm² (or approximately 2426.49 cm²)
Volume = 2880π cm³ (or approximately 9047.78 cm³)
Problem 2:
Surface Area = 452π cm² (or approximately 1420.53 cm²)
Volume = 3000π cm³ (or approximately 9424.78 cm³)
Cone:
Problem 1:
Surface Area = 282π cm² (or approximately 886.54 cm²)
Volume = 400π cm³ (or approximately 1256.64 cm³)
Problem 2:
Surface Area = 87π cm² (or approximately 273.72 cm²)
Volume = 72π cm³ (or approximately 226.20 cm³)
Pyramid:
Problem 1:
Surface Area = 230 cm²
Volume = 233.33 cm³
Problem 2:
Surface Area = 186 cm²
Volume = 108 cm³
Sphere:
Problem 1:
Surface Area = 64π cm² (or approximately 201.06 cm²)
Volume = 268π cm³ (or approximately 841.22 cm³)
Problem 2:
Surface Area = 196π cm² (or approximately 615.75 cm²)
Volume = 1437π cm³ (or approximately 4512.47 cm³)
Hemisphere (without lid):
Problem 1:
Surface Area = 50π cm² (or approximately 157.08 cm²)
Volume = 100π/3 cm³ (or approximately 104.72 cm³)
Problem 2:
Surface Area = 384π cm² (or approximately 1206.37 cm²)
Volume = 2048π/3 cm³ (or approximately 2144.66 cm³)
Hemisphere (with lid):
Problem 1:
Total Surface Area = 1452π cm² (or approximately 4566.33 cm²)
Volume = 1152π/3 cm³ (or approximately 1204.19 cm³)
Problem 2:
Total Surface Area = 576π cm² (or approximately 1809.56 cm²)
Volume = 768π/3 cm³ (or approximately 804.25 cm³)
366.59 cm²
61.49 cm²
20.08 cm²
87.7 cm²
Unit 13 Practice Problems
Cylinder:
Problem 1:
A cylinder has a radius of 8 cm and a height of 15 cm. Calculate its surface area and volume.
Problem 2:
A cylindrical container has a radius of 5 cm and a height of 12 cm. Find its surface area and volume.
Cone:
Problem 1:
A cone has a radius of 6 cm and a slant height of 10 cm. Determine its surface area and volume.
Problem 2:
A cone-shaped party hat has a radius of 3 cm and a height of 8 cm. Find its surface area and volume.
Pyramid:
Problem 1:
A square pyramid has a base side length of 10 cm and a height of 7 cm. Calculate its surface area and volume.
Problem 2:
A pyramid-shaped chocolate has a square base with sides measuring 6 cm, and a height of 9 cm. Find its surface area and volume.
Sphere:
Problem 1:
A sphere has a radius of 4 cm. Calculate its surface area and volume.
Problem 2:
A ball with a perfectly spherical shape has a radius of 7 cm. Determine its surface area and volume.
Hemisphere (without lid):
Problem 1:
A hemisphere has a radius of 5 cm. Determine its surface area and volume, considering only the curved surface and not the flat base.
Problem 2:
A half-sphere-shaped bowl has a radius of 8 cm. Find its surface area and volume, excluding the flat base.
Hemisphere (with lid):
Problem 1:
A hemisphere, including the flat base, has a radius of 12 cm. Calculate its total surface area and volume.
Problem 2:
A decorative glass ornament is shaped like a hemisphere with a radius of 6 cm, including the flat base. Find its total surface area and volume.
Brahmagupta's Formula (For the Area of a Quadrilateral):
Problem 1:
A quadrilateral has side lengths of 8 cm, 10 cm, 12 cm, and 14 cm. Find its area using Brahmagupta's formula.
Problem 2:
A cyclic quadrilateral has side lengths of 6 cm, 7 cm, 9 cm, and 10 cm. Determine its area using Brahmagupta's formula.
Heron's Formula (For the Area of a Triangle):
Problem 1:
A triangle has side lengths of 5 cm, 7 cm, and 9 cm. Calculate its area using Heron's formula.
Problem 2:
A triangle has side lengths of 12 cm, 16 cm, and 20 cm. Find its area using Heron's formula.
Answers
Cylinder:
Problem 1:
Surface Area = 772π cm² (or approximately 2426.49 cm²)
Volume = 2880π cm³ (or approximately 9047.78 cm³)
Problem 2:
Surface Area = 452π cm² (or approximately 1420.53 cm²)
Volume = 3000π cm³ (or approximately 9424.78 cm³)
Cone:
Problem 1:
Surface Area = 282π cm² (or approximately 886.54 cm²)
Volume = 400π cm³ (or approximately 1256.64 cm³)
Problem 2:
Surface Area = 87π cm² (or approximately 273.72 cm²)
Volume = 72π cm³ (or approximately 226.20 cm³)
Pyramid:
Problem 1:
Surface Area = 230 cm²
Volume = 233.33 cm³
Problem 2:
Surface Area = 186 cm²
Volume = 108 cm³
Sphere:
Problem 1:
Surface Area = 64π cm² (or approximately 201.06 cm²)
Volume = 268π cm³ (or approximately 841.22 cm³)
Problem 2:
Surface Area = 196π cm² (or approximately 615.75 cm²)
Volume = 1437π cm³ (or approximately 4512.47 cm³)
Hemisphere (without lid):
Problem 1:
Surface Area = 50π cm² (or approximately 157.08 cm²)
Volume = 100π/3 cm³ (or approximately 104.72 cm³)
Problem 2:
Surface Area = 384π cm² (or approximately 1206.37 cm²)
Volume = 2048π/3 cm³ (or approximately 2144.66 cm³)
Hemisphere (with lid):
Problem 1:
Total Surface Area = 1452π cm² (or approximately 4566.33 cm²)
Volume = 1152π/3 cm³ (or approximately 1204.19 cm³)
Problem 2:
Total Surface Area = 576π cm² (or approximately 1809.56 cm²)
Volume = 768π/3 cm³ (or approximately 804.25 cm³)
366.59 cm²
61.49 cm²
20.08 cm²
87.7 cm²
