Question : The area of the base of a solid cone is 616 cm2. If the height of the cone is 15 cm, then what is the volume of this cone?
Option 1: 2940 cm3
Option 2: 3440 cm3
Option 3: 3190 cm3
Option 4: 3080 cm3
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Correct Answer: 3080 cm3
Solution : Area of the base of the Cone($A$) ⇒ $A$ = πr2 = 616 cm2 and $h$ = 15 cm ⇒ r2 = $\frac{616}{π}$ The formula for the volume ($V$) of a cone is given by: V = $\frac{1}{3}$πr2h, where: $r$ is the radius of the base $h$ is the height ⇒ Volume = $\frac{1}{3}$π $(\sqrt\frac{616}{π})^{2}$ × 15 = $\frac{1}{3}$π$\frac{616}{π}$ × 15 = $\frac{1}{3}$ × 616 × 15 = 3080 cm3 Hence, the correct answer is 3080 cm3.
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Question : The volume of a cone is 27720 cm3. If the height of the cone is 20 cm, then what will be the area of the base?
Option 1: 4158 cm2
Option 2: 4272 cm2
Option 3: 4626 cm2
Option 4: 4836 cm2
Question : The height of a cone is 12 cm and the radius of its base is 14 cm. What is the volume of the cone?
Option 1: 2464 cm3
Option 2: 2692 cm3
Option 3: 2248 cm3
Option 4: 2872 cm3
Question : What is the volume of a cone whose base diameter is 12 cm and the height is 21.7 cm?
Option 1: 626.35 cm3
Option 2: 548.67 cm3
Option 3: 818.07 cm3
Option 4: 334.59 cm3
Question : The curved surface area is thrice as big as the base area of a cone. If the diameter of the cone is 1 cm. Then what is the total surface area (in cm2) of the cone?
Option 1: $\pi$
Option 2: $3\pi $
Option 3: $2\pi$
Option 4: $4\pi $
Question : If the volume of a cube is 5832 cm3, then what is the lateral surface area of this cube?
Option 1: 1024 cm2
Option 2: 384 cm2
Option 3: 576 cm2
Option 4: 1296 cm2
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