Question

worksheet
1 what is the lateral surface area of the cylinder? round to the nearest hundredth.
2 what is the total surface area of the cylinder? round to the nearest hundredth.

1. what is the total surface area of the cylinder? round to the nearest hundredth.
2. what is the lateral surface area of the cylinder? round to the nearest hundredth.
3. what is the lateral surface area of the cylinder? round to the nearest hundredth.
4. what is the total surface area of the cylinder? round to the nearest hundredth.

Explanation:

Let's solve each problem step by step using the formulas for the lateral surface area (\(LSA = 2\pi rh\)) and total surface area (\(TSA = 2\pi r^2 + 2\pi rh\)) of a cylinder, where \(r\) is the radius and \(h\) is the height.

Problem 1: Lateral Surface Area of Cylinder

Given: Radius \(r = 15\) cm, Height \(h = 31\) cm.
Formula: \(LSA = 2\pi rh\)

Step 1: Substitute values into the formula

\(LSA = 2 \times \pi \times 15 \times 31\)

Step 2: Calculate the product

\(LSA = 2 \times \pi \times 465 = 930\pi \approx 930 \times 3.1416 \approx 2921.68\) cm²

Problem 2: Total Surface Area of Cylinder

Given: Radius \(r = 7\) m, Height \(h = 17\) m.
Formula: \(TSA = 2\pi r^2 + 2\pi rh\)

Step 1: Calculate \(2\pi r^2\)

\(2\pi (7)^2 = 2\pi \times 49 = 98\pi\)

Step 2: Calculate \(2\pi rh\)

\(2\pi \times 7 \times 17 = 238\pi\)

Step 3: Sum the two terms

\(TSA = 98\pi + 238\pi = 336\pi \approx 336 \times 3.1416 \approx 1055.58\) m² (Note: The handwritten answer of 828.00 is incorrect; correct calculation shown here.)

Problem 3: Total Surface Area of Cylinder

Given: Radius \(r = 8.2\) in, Height \(h = 12.5\) in.
Formula: \(TSA = 2\pi r^2 + 2\pi rh\)

Step 1: Calculate \(2\pi r^2\)

\(2\pi (8.2)^2 = 2\pi \times 67.24 = 134.48\pi\)

Step 2: Calculate \(2\pi rh\)

\(2\pi \times 8.2 \times 12.5 = 205\pi\)

Step 3: Sum the two terms

\(TSA = 134.48\pi + 205\pi = 339.48\pi \approx 339.48 \times 3.1416 \approx 1066.57\) in² (Note: The handwritten answer of 567.42 is incorrect; correct calculation shown here.)

Problem 4: Lateral Surface Area of Cylinder

Given: Radius \(r = 2.7\) ft, Height \(h = 17.2\) ft.
Formula: \(LSA = 2\pi rh\)

Step 1: Substitute values into the formula

\(LSA = 2 \times \pi \times 2.7 \times 17.2\)

Step 2: Calculate the product

\(LSA = 2 \times \pi \times 46.44 = 92.88\pi \approx 92.88 \times 3.1416 \approx 291.70\) ft² (Note: The handwritten answer of 146.03 is incorrect; correct calculation shown here.)

Problem 5: Lateral Surface Area of Cylinder

Given: Radius \(r = 5\) cm, Height \(h = 7\frac{3}{4} = 7.75\) cm.
Formula: \(LSA = 2\pi rh\)

Step 1: Substitute values into the formula

\(LSA = 2 \times \pi \times 5 \times 7.75\)

Step 2: Calculate the product

\(LSA = 2 \times \pi \times 38.75 = 77.5\pi \approx 77.5 \times 3.1416 \approx 243.47\) cm² (Note: The handwritten answer of 219.91 is incorrect; correct calculation shown here.)

Problem 6: Total Surface Area of Cylinder

Given: Radius \(r = 7\) cm, Height \(h = 12\frac{1}{5} = 12.2\) cm.
Formula: \(TSA = 2\pi r^2 + 2\pi rh\)

Step 1: Calculate \(2\pi r^2\)

\(2\pi (7)^2 = 2\pi \times 49 = 98\pi\)

Step 2: Calculate \(2\pi rh\)

\(2\pi \times 7 \times 12.2 = 170.8\pi\)

Step 3: Sum the two terms

\(TSA = 98\pi + 170.8\pi = 268.8\pi \approx 268.8 \times 3.1416 \approx 844.54\) cm² (Note: The handwritten answer of 898.91 is incorrect; correct calculation shown here.)

Final Answers (Corrected)

1. Lateral Surface Area: \(\boldsymbol{2921.68}\) cm²
2. Total Surface Area: \(\boldsymbol{1055.58}\) m²
3. Total Surface Area: \(\boldsymbol{1066.57}\) in²
4. Lateral Surface Area: \(\boldsymbol{291.70}\) ft²
5. Lateral Surface Area: \(\boldsymbol{243.47}\) cm²
6. Total Surface Area: \(\boldsymbol{844.54}\) cm²

(Note: Handwritten answers in the image contain errors; the above calculations follow the correct formulas for surface area of a cylinder.)

Answer:

Let's solve each problem step by step using the formulas for the lateral surface area (\(LSA = 2\pi rh\)) and total surface area (\(TSA = 2\pi r^2 + 2\pi rh\)) of a cylinder, where \(r\) is the radius and \(h\) is the height.

Problem 1: Lateral Surface Area of Cylinder

Given: Radius \(r = 15\) cm, Height \(h = 31\) cm.
Formula: \(LSA = 2\pi rh\)

Step 1: Substitute values into the formula

\(LSA = 2 \times \pi \times 15 \times 31\)

Step 2: Calculate the product

\(LSA = 2 \times \pi \times 465 = 930\pi \approx 930 \times 3.1416 \approx 2921.68\) cm²

Problem 2: Total Surface Area of Cylinder

Given: Radius \(r = 7\) m, Height \(h = 17\) m.
Formula: \(TSA = 2\pi r^2 + 2\pi rh\)

Step 1: Calculate \(2\pi r^2\)

\(2\pi (7)^2 = 2\pi \times 49 = 98\pi\)

Step 2: Calculate \(2\pi rh\)

\(2\pi \times 7 \times 17 = 238\pi\)

Step 3: Sum the two terms

\(TSA = 98\pi + 238\pi = 336\pi \approx 336 \times 3.1416 \approx 1055.58\) m² (Note: The handwritten answer of 828.00 is incorrect; correct calculation shown here.)

Problem 3: Total Surface Area of Cylinder

Given: Radius \(r = 8.2\) in, Height \(h = 12.5\) in.
Formula: \(TSA = 2\pi r^2 + 2\pi rh\)

Step 1: Calculate \(2\pi r^2\)

\(2\pi (8.2)^2 = 2\pi \times 67.24 = 134.48\pi\)

Step 2: Calculate \(2\pi rh\)

\(2\pi \times 8.2 \times 12.5 = 205\pi\)

Step 3: Sum the two terms

\(TSA = 134.48\pi + 205\pi = 339.48\pi \approx 339.48 \times 3.1416 \approx 1066.57\) in² (Note: The handwritten answer of 567.42 is incorrect; correct calculation shown here.)

Problem 4: Lateral Surface Area of Cylinder

Given: Radius \(r = 2.7\) ft, Height \(h = 17.2\) ft.
Formula: \(LSA = 2\pi rh\)

Step 1: Substitute values into the formula

\(LSA = 2 \times \pi \times 2.7 \times 17.2\)

Step 2: Calculate the product

\(LSA = 2 \times \pi \times 46.44 = 92.88\pi \approx 92.88 \times 3.1416 \approx 291.70\) ft² (Note: The handwritten answer of 146.03 is incorrect; correct calculation shown here.)

Problem 5: Lateral Surface Area of Cylinder

Given: Radius \(r = 5\) cm, Height \(h = 7\frac{3}{4} = 7.75\) cm.
Formula: \(LSA = 2\pi rh\)

Step 1: Substitute values into the formula

\(LSA = 2 \times \pi \times 5 \times 7.75\)

Step 2: Calculate the product

\(LSA = 2 \times \pi \times 38.75 = 77.5\pi \approx 77.5 \times 3.1416 \approx 243.47\) cm² (Note: The handwritten answer of 219.91 is incorrect; correct calculation shown here.)

Problem 6: Total Surface Area of Cylinder

Given: Radius \(r = 7\) cm, Height \(h = 12\frac{1}{5} = 12.2\) cm.
Formula: \(TSA = 2\pi r^2 + 2\pi rh\)

Step 1: Calculate \(2\pi r^2\)

\(2\pi (7)^2 = 2\pi \times 49 = 98\pi\)

Step 2: Calculate \(2\pi rh\)

\(2\pi \times 7 \times 12.2 = 170.8\pi\)

Step 3: Sum the two terms

\(TSA = 98\pi + 170.8\pi = 268.8\pi \approx 268.8 \times 3.1416 \approx 844.54\) cm² (Note: The handwritten answer of 898.91 is incorrect; correct calculation shown here.)

Final Answers (Corrected)

1. Lateral Surface Area: \(\boldsymbol{2921.68}\) cm²
2. Total Surface Area: \(\boldsymbol{1055.58}\) m²
3. Total Surface Area: \(\boldsymbol{1066.57}\) in²
4. Lateral Surface Area: \(\boldsymbol{291.70}\) ft²
5. Lateral Surface Area: \(\boldsymbol{243.47}\) cm²
6. Total Surface Area: \(\boldsymbol{844.54}\) cm²

(Note: Handwritten answers in the image contain errors; the above calculations follow the correct formulas for surface area of a cylinder.)