the radius and the slant height of a cone are in the ratio of 4:7.if its curve surface area is 792 cm square find its radius
Answers
HI,
THE CHAPTER:-SURFACE,AREAS AND VOLUMES
THE ANSWER:-
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Given, the radius and slant height of a cone is in the ratio of 4:7
Let the radius of the cone = 4x
and the slant height of the cone = 7x
Given, curved surface area of the cone = 792
=> πrl = 792
=> (22/7)*4x * 7x = 792
=> 88x2 = 792
=> x2 = 792/88
=> x2 = 9
=> x = √9
=> x = 3
So, the radius of the circle = 4x = 4*3 = 12 cm
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Step-by-step explanation:
Given
The radius and slant of height of a cone are in the ratio 4:7
Curved Surface Area is 792 cm²
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To Find
The radius
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Solution
Let's consider the radius to be '4x' and height be '7x' (Here we have taken the radius as 4x and 7x since they are in the ratio of 4:7)
Formula to find the curved surface area of a cone ⇒ πrl
Here,
'r' stands for radius.
'l' stands for the slant height.
Curved surface area of the cone ⇒ 729 cm²
Let's solve the equation step-by-step
22/7×4x×7x =792
Step 1: Simplify the equation.
⇒ 22/7 4x × 7x = 729
⇒22/7×28x² =729
=22×4x²= 792
=88x²=792
Step 2: Divide 88 from both sides of the equation.
⇒ 88x²/88 = 792/88
Step 3: Find the square root of 9.
⇒ x=√9
= x=3
∴ The radius ⇒ 4x ⇒ 4(3) ⇒ 12 cm
∴ The slant height of cone ⇒ 7x ⇒ 7(3) ⇒ 21 cm
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