1. A milk can has a radius of 5 cm and a height of 10 cm. How much tin was used in making it?
2. A closed cone model has a radius of 8 cm and a height of 15 cm. Find the amount of material used in making the cone.
3. Teresa has a box made of wood in the shape of a cube whose side is 7 decimeters. She wants to paint it all over in the outside. How much area will be painted?
4. How much gift wrapper is needed to wrap a box 22 cm long, 12 cm wide and 7 cm high?
5. A ball made of rubber has a radius of 10 cm. What is the surface area of the rubber material of which it is made?
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Answers & Comments
1.A milk can has a radius of 5 cm and a height of 10 cm. How much tin was used in making it?
The area of the circular top and bottom can be calculated using the formula for the area of a circle:
A = πr²
where A is the area, and r is the radius. Since the milk can has a radius of 5 cm, the area of each circular end is:
A1 = A2 = π(5 cm)² = 25π cm²
The area of the curved side can be calculated using the formula for the lateral surface area of a cylinder:
A = 2πrh
where A is the area, r is the radius, and h is the height. Since the milk can has a radius of 5 cm and a height of 10 cm, the area of the curved side is:
A3 = 2π(5 cm)(10 cm) = 100π cm²
Therefore, the total surface area of the milk can is:
A = A1 + A2 + A3 = 25π cm² + 25π cm² + 100π cm² = 150π cm²
So, the amount of tin used in making the milk can is 150π square centimeters.
2.A closed cone model has a radius of 8 cm and a height of 15 cm. Find the amount of material used in making the cone.
The area of the base of the cone can be calculated using the formula for the area of a circle:
A = πr²
where A is the area, and r is the radius. Since the cone has a radius of 8 cm, the area of its base is:
A1 = π(8 cm)² = 64π cm²
The area of the curved side can be calculated using the formula for the lateral surface area of a cone:
A = πrs
where A is the area, r is the radius, and s is the slant height. The slant height can be calculated using the Pythagorean theorem:
s = √(r² + h²) = √(8² + 15²) = √289 = 17 cm
So, the area of the curved side is:
A2 = π(8 cm)(17 cm) = 136π cm²
Therefore, the total surface area of the cone is:
A = A1 + A2 = 64π cm² + 136π cm² = 200π cm²
So, the amount of material used in making the cone is 200π square centimeters.
3. Teresa has a box made of wood in the shape of a cube whose side is 7 decimeters. She wants to paint it all over in the outside. How much area will be painted?
The surface area of a cube can be found by using the formula:
A = 6s²
where A is the surface area and s is the length of the side of the cube.
In this case, the side of the cube is 7 decimeters. So, the surface area of the cube is:
A = 6(7 dm)² = 6(49 dm²) = 294 dm²
Therefore, Teresa will need to paint 294 square decimeters of wood to cover the entire outside of the cube.
4.How much gift wrapper is needed to wrap a box 22 cm long, 12 cm wide and 7 cm high?
The surface area of a rectangular box can be found using the formula:
A = 2lw + 2lh + 2wh
where A is the surface area, l is the length, w is the width, and h is the height of the box.
In this case, the length of the box is 22 cm, the width is 12 cm, and the height is 7 cm. So, the surface area of the box is:
A = 2(22 cm x 12 cm) + 2(22 cm x 7 cm) + 2(12 cm x 7 cm)
A = 2(264 cm²) + 2(154 cm²) + 2(84 cm²)
A = 1056 cm² + 308 cm² + 168 cm²
A = 1532 cm²
Therefore, 1532 square centimeters of gift wrapper are needed to wrap the box.
5. A ball made of rubber has a radius of 10 cm. What is the surface area of the rubber material of which it is made?
The surface area of a sphere can be found using the formula:
A = 4πr²
where A is the surface area, and r is the radius of the sphere.
In this case, the radius of the ball is 10 cm. So, the surface area of the rubber material of which it is made is:
A = 4π(10 cm)² = 400π cm²
Therefore, the surface area of the rubber material of which the ball is made is 400π square centimeters.
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