Unit 11 Volume and Surface Area Homework 3 Answers
Introduction
Welcome to the third edition of the Unit 11 Volume and Surface Area Homework Answers series. In this article, we will be providing you with the answers to the homework questions from Unit 11, which focuses on volume and surface area. Whether you're a student looking for some extra help or a teacher searching for a resource to assist your students, this article is here to provide you with the answers you need.
Question 1: Finding the Volume of a Rectangular Prism
To find the volume of a rectangular prism, you need to multiply its length, width, and height. The formula for finding the volume of a rectangular prism is V = lwh. Let's take a look at an example:
Example: Find the volume of a rectangular prism with length = 5 cm, width = 3 cm, and height = 4 cm.
Solution: V = 5 cm x 3 cm x 4 cm = 60 cm³
Question 2: Finding the Surface Area of a Cylinder
The surface area of a cylinder can be found by adding the areas of its two bases and its lateral surface area. The formula for finding the surface area of a cylinder is SA = 2πr² + 2πrh. Let's solve an example:
Example: Find the surface area of a cylinder with radius = 4 cm and height = 8 cm.
Solution: SA = 2π(4 cm)² + 2π(4 cm)(8 cm) = 32π + 64π = 96π cm²
Question 3: Finding the Volume of a Cone
The volume of a cone can be found by multiplying the area of its base by the height and dividing the result by 3. The formula for finding the volume of a cone is V = (1/3)πr²h. Let's work through an example:
Example: Find the volume of a cone with radius = 6 cm and height = 10 cm.
Solution: V = (1/3)π(6 cm)²(10 cm) = 120π cm³
Question 4: Finding the Surface Area of a Sphere
The surface area of a sphere can be found by multiplying its radius squared by 4π. The formula for finding the surface area of a sphere is SA = 4πr². Let's find the surface area of a sphere in an example:
Example: Find the surface area of a sphere with radius = 5 cm.
Solution: SA = 4π(5 cm)² = 100π cm²
Question 5: Finding the Volume of a Triangular Prism
The volume of a triangular prism can be found by multiplying the area of its base triangle by its height. The formula for finding the volume of a triangular prism is V = (1/2)bh. Let's solve an example:
Example: Find the volume of a triangular prism with base length = 6 cm, base width = 4 cm, and height = 10 cm.
Solution: V = (1/2)(6 cm)(4 cm)(10 cm) = 120 cm³
Question 6: Finding the Surface Area of a Rectangular Prism
The surface area of a rectangular prism can be found by adding the areas of its six faces. The formula for finding the surface area of a rectangular prism is SA = 2lw + 2lh + 2wh. Let's work through an example:
Example: Find the surface area of a rectangular prism with length = 8 cm, width = 5 cm, and height = 6 cm.
Solution: SA = 2(8 cm)(5 cm) + 2(8 cm)(6 cm) + 2(5 cm)(6 cm) = 188 cm²
Question 7: Finding the Volume of a Cylinder
The volume of a cylinder can be found by multiplying the area of its base by its height. The formula for finding the volume of a cylinder is V = πr²h. Let's solve an example:
Example: Find the volume of a cylinder with radius = 3 cm and height = 10 cm.
Solution: V = π(3 cm)²(10 cm) = 90π cm³
Question 8: Finding the Surface Area of a Cone
The surface area of a cone can be found by adding the area of its base and its lateral surface area. The formula for finding the surface area of a cone is SA = πr² + πrl. Let's find the surface area of a cone in an example:
Example: Find the surface area of a cone with radius = 7 cm and slant height = 10 cm.
Solution: SA = π(7 cm)² + π(7 cm)(10 cm) = 49π + 70π = 119π cm²
Question 9: Finding the Volume of a Sphere
The volume of a sphere can be found by multiplying the radius cubed by (4/3)π. The formula for finding the volume of a sphere is V = (4/3)πr³. Let's work through an example:
Example: Find the volume of a sphere with radius = 6 cm.
Solution: V = (4/3)π(6 cm)³ = 288π cm³
Question 10: Finding the Surface Area of a Triangular Prism
The surface area of a triangular prism can be found by adding the areas of its three rectangular faces and the areas of its two triangular faces. Let's solve an example:
Example: Find the surface area of a triangular prism with base length = 8 cm, base width = 6 cm, and height = 12 cm.
Solution: SA = 2lw + 2lh + 2wh = 2(8 cm)(6 cm) + 2(8 cm)(12 cm) + 2(6 cm)(12 cm) = 432 cm²
Question 11: Finding the Volume of a Pyramid
The volume of a pyramid can be found by multiplying the area of its base by its height and dividing the result by 3. The formula for finding the volume of a pyramid is V = (1/3)Bh, where B is the area of the base. Let's find the volume of a pyramid in an example:
Example: Find the volume of a pyramid with base length = 10 cm, base width = 6 cm, and height = 8 cm.
Solution: V = (1/3)(10 cm)(6 cm)(8 cm) = 160 cm³
Question 12: Finding the Surface Area of a Rectangular Pyramid
The surface area of a rectangular pyramid can be found by adding the areas of its four triangular faces and the area of its base. The formula for finding the surface area of a rectangular pyramid is SA = B + 2lw + 2lh + 2wh, where B is the area of the base. Let's solve an example:
Example: Find the surface area of a rectangular pyramid with base length = 8 cm, base width = 6 cm, and slant height = 10 cm.
Solution: SA = B + 2lw + 2lh + 2wh = 2(8 cm)(6 cm) + 2(8 cm)(10 cm) + 2(6 cm)(10 cm) = 316 cm²
Question 13: Finding the Volume of a Cone Frustum
The volume of a cone frustum can be found by subtracting the smaller cone's volume from the larger cone's volume. The formula for finding the volume of a cone frustum is V = (1/3)πh(R² + r² + Rr), where R is the radius of the larger base, r is the radius of the smaller base, and h is the height. Let's work through an example:
Example: Find the volume of a cone frustum with larger base radius = 10 cm, smaller base radius = 6 cm, and height = 12 cm.
Solution: V = (1/3)π(12 cm)((10 cm)² + (6 cm)² + (10 cm)(6 cm)) = 720π cm³
Question 14: Finding the Surface Area of a Sphere Segment
The surface area of a sphere segment can be found by adding the areas of its base circle and its curved surface. The formula for finding the surface area of a sphere segment is SA = 2πrh + πr², where r is the radius of the sphere and h is the height of the segment. Let's find the surface area of a sphere segment in an example: