If the surface area of sphere is 616 cm2, find its radius. \(\left(\text{Use } \pi=\frac{22}{7}\right)\)
7 cm
Surface area of a sphere = \( 4\pi r^2 \).
\( 4\times\frac{22}{7}\times r^2=616\Rightarrow r^2=\frac{616\times7}{88}=49 \).
\( r=\sqrt{49}=7 \) cm.
Hence, the radius of the sphere is 7 cm.
A 60 cm diameter cylinder that is rolling without sliding at a rate of 7 rounds per second. How much distance will the cylinder roll in 15 seconds? \(\left(\text{Use } \pi = \frac{22}{7}\right)\)
In a right circular cone, the base has a radius of 4.2 cm and the height is 30 cm. A cross- section is made at the midpoint of the height, parallel to the base. Find the volume of the smaller cone between the cross-section and the vertex. (Use π = 22/7)
The volume of a closed rectangular box is 7500 cm3, and its dimensions are in the ratio 3:4:5. The box is to be painted on all outer surfaces at a rate of ₹4/cm2. If an 18% GST is applied on the painting cost, what is the total amount to be paid?
Ragini had to make a model of a cylindrical kaleidoscope for her science project. She wanted to use chart paper to make the curved surface of the kaleidoscope. What would be the area of chart paper required by her, if she wanted to make a kaleidoscope of length 55 cm with a 14 cm radius? (Use \(\pi = \frac{22}{7}\))
A cylindrical tank of radius 7 cm can contain 2156 cm3 of water. What is its height? (Take \(\pi = \frac{22}{7}\))
The radius of the base of a cone is 7 cm and its slant height is 25 cm. The entire outer surface of the cone is to be painted at the rate of ₹2 per cm². What is the total cost of painting the cone? \(\left(\text{Use } \pi=\frac{22}{7}\right)\)
A cylindrical pillar is 20 cm in diameter and 35 m in height. Find the cost of painting the curved surface of the pillar at the rate of ₹30 per m2.
\(\left(\text{Use } \pi=\frac{22}{7}\right)\)
A cylindrical pillar is 80 cm in diameter and 35 m in height. Find the cost of painting the curved surface of the pillar at the rate of ₹45 per m2. (Use \(\pi = \frac{22}{7}\))
The volume of a cone is 1540 cm3 and radius is 7 cm. What is the height of the cone?
A solid cone has a height of 24 cm and a base radius of 7 cm. It is cut by a plane parallel to the base at a point 16 cm from the vertex. After removing the smaller cone, the remaining frustum is obtained. Find the total surface area of the frustum.
A cone and a hemisphere have equal bases and volumes. What is the ratio of the height of the cone to the radius of the hemisphere?
A cube is 7 cm of an edge and another cube is 14 cm on an edge. The ratios of their surface areas are
Using three distinct points which of the following shapes cannot be formed?
Two cubes each of edge 12 cm are joined end to end. Find the surface area of the resulting cuboid.
The areas of three adjacent faces of a cuboid are x, y, z. If the volume is V, then V 2will be equal to: