Math Trivia Quiz On Mensuration!

The curved surface area of a right circular cylinder is given by the formula 2πrh, where r is the radius and h is the height. In this case, the radius and height are both 1cm. Plugging these values into the formula, we get 2π(1)(1) = 2π. Therefore, the curved surface area is equal to 2π, which corresponds to option (2).

The curved surface area of a right circular cylinder can be calculated using the formula 2πrh, where r is the radius and h is the height. In this case, the radius is a units and the height is b units, so the curved surface area is 2πab sq.cm.

The slant height of a right circular cone can be found using the Pythagorean theorem. The slant height is the hypotenuse of a right triangle formed by the height, the radius (which is half the diameter), and the slant height. In this case, the height is 8 cm and the radius is 6 cm (half of the diameter of 12 cm). Using the Pythagorean theorem, we can calculate the slant height as follows: slant height = √(8^2 + 6^2) = √(64 + 36) = √100 = 10 cm. Therefore, the correct answer is 10 cm.

The ratio of the surface areas of two spheres is equal to the square of the ratio of their radii. Since the surface area is proportional to the square of the radius, the ratio of the volumes of the spheres will be equal to the cube of the ratio of their radii. Therefore, the volume ratio of the spheres will be 27:125.

The volume of a right circular cylinder is calculated by multiplying the base area by the height. In this case, the base area is given as 80 and the height is given as 5. Therefore, the volume can be calculated as 80 * 5 = 400 cm^3.

The formula for the surface area of a sphere is 4πr^2, where r is the radius of the sphere. In this case, the surface area is given as 36π. By equating this to the formula, we can solve for r: 4πr^2 = 36π. Dividing both sides by 4π gives us r^2 = 9, and taking the square root of both sides gives r = 3.

The formula for the volume of a sphere is (4/3)πr^3. Plugging in the value of r as 3, we get (4/3)π(3^3) = 36π. Therefore, the volume of the sphere is 36π cm^3.

The total surface area of a solid right circular cylinder is given by the formula 2πr(r+h), where r is the radius and h is the height. In this case, the total surface area is given as 200π and the radius is given as 5 cm. We can substitute these values into the formula and solve for the sum of the height and radius. 2π(5)(5+h) = 200π. Simplifying the equation, we get 10(5+h) = 100, which simplifies further to 50 + 10h = 100. Solving for h, we get h = 5. Therefore, the sum of the height and radius is 5 + 5 = 10 cm.

The volume of a right circular cone is equal to one-third the volume of a right circular cylinder with the same base area and height. Since the radius and height of the cone and cylinder are equal, the base area and height of both shapes are also equal. Therefore, the volume of the cone is one-third of the volume of the cylinder, which is 120 cm^3. Hence, the volume of the cone is 40 cm^3.

The ratio of the slant heights of the two cones is 4:3. The curved surface area of a cone is directly proportional to its slant height. Therefore, if the ratio of the slant heights is 4:3, then the ratio of their respective curved surface areas will also be 4:3.

The surface area of a sphere is given by the formula 4πr^2, where r is the radius of the sphere. In this case, the surface area is given as 100π. By equating the formula to the given surface area, we can solve for the radius. 4πr^2 = 100π. Dividing both sides by 4π, we get r^2 = 25. Taking the square root of both sides, we find that r = 5. Therefore, the radius of the sphere is 5 cm.

The volume of a cone can be calculated using the formula V = (1/3)πr^2h, where r is the radius of the base and h is the height of the cone. In this case, the base area is given as 48 sq.cm, which means the radius can be calculated as √(48/π) cm. Since the height is given as 5 cm, we can substitute these values into the formula to find the volume. After performing the calculations, we find that the volume of the cone is 80 cm^3.

The respective volumes of the two cylinders can be found by multiplying the respective heights and the respective radii squared. Since the ratio of the heights is 1:2 and the ratio of the radii is 2:1, we can calculate the ratio of the volumes as (1/2)^2 : (2/1)^2, which simplifies to 1:4. Therefore, the correct answer is 1:4.

The volume of a cone is given by the formula V = (1/3)πr^2h, where r is the radius of the base and h is the height of the cone. The base area of the cone is given by the formula A = πr^2. Given that the volume is 48π and the base area is 12π, we can set up the following equation: (1/3)πr^2h = 48π and πr^2 = 12π. By dividing the second equation by π, we get r^2 = 12. Taking the square root of both sides, we get r = √12 = 2√3. Substituting this value of r into the first equation, we get (1/3)π(2√3)^2h = 48π. Simplifying, we get (1/3)(4)(3)h = 48. Solving for h, we get h = 12 cm.

The total surface area of a solid hemisphere can be calculated by adding the curved surface area of the hemisphere and the area of the circular base. The curved surface area of a hemisphere is given by half the surface area of a sphere, which is 2πr^2. The area of the circular base is given by πr^2.

In this case, the diameter of the hemisphere is 2 cm, so the radius is 1 cm.

The curved surface area of the hemisphere is 2π(1^2) = 2π cm^2.
The area of the circular base is π(1^2) = π cm^2.

Adding these two areas together, we get 2π + π = 3π cm^2.

Therefore, the correct answer is 3π cm^2.

The formula for the curved surface area of a cone is given by πrℓ, where r is the radius of the base and ℓ is the slant height. In this question, the circumference at the base is given as 120π cm, which means the radius is 120π/2π = 60 cm. The slant height is given as 10 cm. Plugging these values into the formula, we get π(60)(10) = 600π cm^2. Therefore, the curved surface area of the cone is 600π cm^2.

The formula for the curved surface area of a sphere is 4πr^2, where r is the radius of the sphere. In this case, the radius is given as 2 cm. Plugging the value into the formula, we get 4π(2^2) = 4π(4) = 16π cm^2. Therefore, the correct answer is 16 π cm^2.

The total surface area of a solid hemisphere can be found by adding the curved surface area of the hemisphere and the area of the base. The curved surface area of a hemisphere is given by 2πr^2, where r is the radius. The area of the base is equal to the area of a circle with radius r, which is πr^2. Adding these two values gives us the total surface area of the solid hemisphere, which is 3πr^2. Therefore, the correct answer is 3πa^2 cm^2.

If the radius of one sphere is half of the radius of another sphere, their respective volumes can be calculated using the formula V = (4/3)πr^3. Since the radius is half, the volume of the smaller sphere will be (4/3)π(1/2r)^3 = (1/8)(4/3)πr^3. This means that the volume of the smaller sphere is 1/8th of the volume of the larger sphere. Therefore, the correct answer is 1:8.

The curved surface area of a solid hemisphere is half of the total surface area of the hemisphere. Therefore, if the total surface area is 12π, then the curved surface area would be half of that, which is 6π. However, none of the given answer choices match this value. Therefore, the correct answer is not available.

The total surface area of a solid right circular cylinder is given by the formula 2πrh + 2πr^2, where r is the radius and h is the height. In this case, the radius is half the height, so we can substitute r = h/2 into the formula. Plugging in these values, we get 2π(h/2)(h) + 2π(h/2)^2 = πh^2 + πh^2/2 = 3/2πh^2. Therefore, the correct answer is 3/2πh^2 sq.cm.

The volume of a sphere is given by the formula V = (4/3)πr^3, where V is the volume and r is the radius. In this case, the volume is given as π cu.cm. By equating the given volume to the formula, we can solve for the radius. Rearranging the formula, we get r^3 = (3/4) cu.cm. Taking the cube root of both sides, we find that r = 3/4 cm. Therefore, the correct answer is 3/4 cm.

When a solid sphere is divided into two hemispheres, the curved surface area of one hemisphere is equal to half of the curved surface area of the sphere. Therefore, the curved surface area of one hemisphere would be 24/2 = 12 cm^2. However, the given options do not include 12 cm^2, so the correct answer must be the closest option, which is 18 cm^2.