Ask Question
9 September, 03:15

What is the surface area of a cone that has a slant height of 18.5 inches and a radius of 11 inches?

+3
Answers (2)
  1. 9 September, 03:48
    0
    Answer: The answer is C. 324.5

    Step-by-step explanation:

    correct on edge
  2. 9 September, 04:17
    0
    Where,

    r is the radius

    h is the height

    l is the slant height

    The area of the curved (lateral) surface of a cone = πrl

    Note:

    A cone does not have uniform (or congruent) cross-sections. (more about conic section here)

    Example 1: A cone has a radius of 3cm and height of 5cm, find total surface area of the cone.

    Solution:

    To begin with we need to find slant height of the cone, which is determined by using Pythagoras, since the cross section is a right triangle.

    l2 = h2 + r2

    l2 = 52 + 32

    l2 = 25 + 9

    l = √ (34)

    l = 5.83 cm

    And the total surface area of the cone is:

    SA = πr2 + πrl

    SA = π · r · (r + l)

    SA = π · 3 · (3 + 5.83)

    SA = 83.17 cm2

    Therefore, the total surface area of the cone is 83.17cm2

    Example 2: The total surface area of a cone is 375 square inches. If its slant height is four times the radius, then what is the base diameter of the cone? Use π = 3.

    Solution:

    The total surface area of a cone = πrl + πr2 = 375 inch2

    Slant height: l = 4 * radius = 4r

    Substitute l = 4r and π = 3

    3 * r * 4 r + 3 * r2 = 375

    12r2 + 3r2 = 375

    15r2 = 375

    r2 = 25

    r = 25

    r = 5

    So the base radius of the cone is 5 inch.

    And the base diameter of the cone = 2 * radius = 2 * 5 = 10 inch.

    Example 3: What is the total surface area of a cone if its radius = 4cm and height = 3 cm.

    Solution:

    As mentioned earlier the formula for the surface area of a cone is given by:

    SA = πr2 + πrl

    SA = πr (r + l)

    As in the previous example the slant can be determined using Pythagoras:

    l2 = h2 + r2

    l2 = 32 + 42

    l2 = 9 + 16

    l = 5

    Insert l = 5 we will get:

    SA = πr (r + l)

    SA = 3.14 · 4 · (4+5)

    SA = 113.04 cm2

    Example 4: The slant height of a cone is 20cm. the diameter of the base is 15cm. Find the curved surface area of cone.

    Solution:

    Given that,

    Slant height: l = 20cm

    Diameter: d = 15cm

    Radius: r = d/2 = 15/2 = 7.5cm

    Curved surface area = πrl

    CSA = πrl

    CSA = π · 7.5 · 20

    CSA = 471.24 cm2

    Example 5: Height and radius of the cone is 5 yard and 7 yard. Find the lateral surface area of the given cone.

    Solution:

    Lateral surface area of the cone = πrl

    Step 1:

    Slant height of the cone:

    l2 = h2 + r2

    l2 = 72 + 52

    l2 = 49 + 25

    l = 8.6

    Step 2: Lateral surface area:

    LSA = πrl

    LSA = 3.14 * 7 * 8.6

    LSA = 189.03 yd2

    So, the lateral surface area of the cone = 189.03 squared yard.

    Example 6: A circular cone is 15 inches high and the radius of the base is 20 inches What is the lateral surface area of the cone?

    Solution:

    The lateral surface area of cone is given by:

    LSA = π * r * l

    LSA = 3.14 * 20 * 15

    LSA = 942 inch2

    Example 7: Find the total surface area of a cone, whose base radius is 3 cm and the perpendicular height is 4 cm.

    Solution:

    Given that:

    r = 3 cm

    h = 4 cm

    To find the total surface area of the cone, we need slant height of the cone, instead the perpendicular height.

    The slant height l can be found by using Pythagoras theorem.

    l2 = h2 + r2

    l2 = 32 + 42

    l2 = 9 + 16

    l = 5

    The total surface area of the cone is therefore:

    SA = πr (r + l)

    SA = 3.14 · 3 · (3+5)

    SA = 75.36 cm2
Know the Answer?
Not Sure About the Answer?
Get an answer to your question ✅ “What is the surface area of a cone that has a slant height of 18.5 inches and a radius of 11 inches? ...” in 📙 Mathematics if there is no answer or all answers are wrong, use a search bar and try to find the answer among similar questions.
Search for Other Answers