MATHEMATICS HIGH SCHOOL

The volumes of two similar solids are 1,728 m^3 and 343 m^3. The surface area of the larger solid is 576 m^2. What is the surface area of the smaller solid? a. 196 m^2 b. 76m^2 c. 1,372m^2 d. 392 m^2

Answers

Answer 1

Answer:

Answer:

Option a. 196 m²

Step-by-step explanation:

Volumes of two similar solids are 1728 m³ and 343 m³

So the ratio of these volumes = $(343)/(1728)$

Now we know volume is a three dimensional unit so we find the cube root of the ratio of the volumes to find the ratio of sides.

Scale factor = $\sqrt[3]{(343)/(1728) }=(7)/(12)$

Now we know area of solids is a two dimensional unit so we will square the scale factor and this will be the ratio of area

(Scale factor)² = $((7)/(12))^(2)$ = (Surface area of smaller solid)/(surface area of larger solid)

Area of larger solid = 576 m²

$((7)/(12))^(2)=(S)/(576)$

$S=(49)/(144).(576)=(49).(4)=196$

Surface area of of the smaller solid = 196 m²

Option A. is the answer.

Answer 2

Answer: Scale factor = (1728/343)^(1/3) = 12/7 Let the surface area of the smaller solid be A, then: A * (12/7)^2 = 576 So A = 196

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Answers

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Answer:

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Step-by-step explanation:

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Answers

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THE VOLUME OF A CONE IS 15 PI CUBIC METERS. WHAT IS THE VOLUME OF A CYLINDER HAVING THE SAME BASE AND SAME HEIGHT?

Answers

Okay, so I know that you either multiply the volume of a cone by 3 to get the cylinders volume, or you divide it. I think you multiply it. Just remember, the rule is to multiply the volume of a cone by 3, to get the cylinder volume with the same measurements. So 15 x 3.

Final answer:

To find the volume of a cone and a cylinder with the same base and height, use the formulas for volume of a cone and volume of a cylinder. Solve for r^2 * h in the cone's volume formula, then use this value in the cylinder's volume formula.

Explanation:

To find the volume of the cylinder with the same base and height as the given cone, we need to know the formula for the volume of a cone and the formula for the volume of a cylinder. The volume of a cone is given by the formula V = 1/3 * π * r^2 * h, where r is the radius of the base and h is the height of the cone. Since the cone has a volume of 15π cubic meters, we can set up the equation 15π = 1/3 * π * r^2 * h and solve for r^2 * h. Once we have r^2 * h, we can use the formula for the volume of a cylinder, V = π * r^2 * h, to calculate the volume of the cylinder.

, let's solve the equation 15π = 1/3 * π * r^2 * h for r^2 * h:

15π = 1/3 * π * r^2 * h

Multiplying both sides of the equation by 3, we get:

45π = π * r^2 * h

Canceling out the π on both sides of the equation, we get:

45 = r^2 * h

Now we have r^2 * h, which is 45. Let's plug this value into the formula for the volume of a cylinder, V = π * r^2 * h:

V = π * 45

So the volume of the cylinder with the same base and height as the given cone is 45π cubic meters.

Learn more about Volume of Cone and Cylinder here:

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Answers

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