## Surface Areas and Volumes

### Important Questions

Q) A tent is in the shape of a right circular cylinder up to a height of 3 m and then a right circular cone,…

Q) A solid wooden toy is in the shape of a right circular cone mounted on a hemisphere of same radius. If the radius of…

Q) The word ‘circus’ has the same root as ‘circle’. In a closed circular area, various entertainment acts including human skill and animal training are…

Q) A wooden toy is made by scooping out a hemisphere of same radius as of cylinder, from each end of a wooden solid cylinder. If…

Q) Determine the ratio of the volume of a cube to that of the sphere which will exactly fit inside the cube. Ans. Let’s draw…

Q) The interior of a building is in the form of a cylinder of base radius 12 m and height 3.5 m surmounted by a…

Q) The difference between the outer and inner radii of a hollow right circular cylinder of length 14 cm is 1 cm. If the volume…

Q) A vessel is in the form of a hollow hemisphere mounted by a hollow cylinder. The diameter of the hemisphere is 14 cm and…

Q) The slant height of a frustum of a cone is 4 cm and the perimeters of its circular ends are 18 cm and 6…

Q) 21 glass spheres, each of radius 2 cm are packed in a cuboidal box of internal dimensions 16 cm × 8 cm × 8…

Q) A well of diameter 3m is dug 14m deep. The earth taken out of it has been evenly spread out in the form of…

Q) A gulab jamun, contains sugar syrup up to about 30% of its volume. Find approximately how much syrup would be found in 45 gulab jamuns,…

Q) A medicine capsule is in the shape of a cylinder with two hemispheres stuck to each of its ends. The length of the entire…

Q: A group of students of class X visited India Gate on an education trip. The teacher and students had interest in history as well.…

Q: On a Sunday, your Parents took you to a fair. You could see lot of toys displayed, and you wanted them to buy a…

Q) The Great Stupa at Sanchi is one of the oldest stone structures in India, and an important monument of Indian Architecture. It was originally…

Q) Adventure camps are the perfect place for the children to practice decision making for themselves without parents and teachers guiding their every move. Some…

Q) Water in a canal, 8 m wide and 6 m deep, is flowing with a speed of 12 km/hour. How much area will it…

Q) From a solid cylinder of height 30 cm and radius 7 cm, a conical cavity of height 24 cm and same radius is hollowed…

Q) A rocket is in the form of a right circular cylinder closed at the lower end and surmounted by a cone with the same…

Q) 150 spherical marbles, each of diameter 1.4 cm, are dropped in a cylindrical vessel of diameter 7 cm containing some water, which are completely…

Q) Shanta runs an industry in a shed which was in the shape of a cuboid surmounted by half cylinder. The dimensions of the base…

Q) A tent is in the shape of a cylinder surmounted by a conical top. If the height and radius of the cylindrical part are…

Q) Water is flowing at the rate of 15 km/h through a pipe of diameter 14 cm into a cuboidal pond which is 50 m…

Q) A golf ball is spherical with about 300 – 500 dimples that help increase its velocity while in play. Golf balls are traditionally white…

Q) A wooden article was made by scooping out a hemisphere from each end of a solid cylinder, as shown in the figure. If the…

Q) From a solid cylinder of height 20 cm and diameter 12 cm, a conical cavity of height 8 cm and radius 6 cm is…

Q) Governing council of a local public development authority of Dehradun decided to build an adventurous playground on the top of a hill, which will…

Q) A student was asked to make a model like a cylinder with two cones attached to its ends by using a thin aluminium sheet.…

Q) Reeti prepares a rakhi for her brother Ronit. The Rakhi consists of a rectangle of length 8 cm and breadth 6 cm inscribed in…

Q) In a coffee shop, coffee is served in two types of cups. One is cylindrical in shape with diameter 7 cm and height 14…

Q) Can any rational value of x make the new area equal to 220cm2 ? Ans: If by increasing each dimension by x units, the…

Q) While designing the school year book, a teacher asked the student that the length and width of a particular photo is increased by x…

Q) A room is in the form of cylinder surmounted by a hemi-spherical dome. The base radius of hemisphere is one-half the height of cylindrical…

Q) An empty cone is of radius 3 cm and height 12 cm. Ice-cream is filled in it so that lower part of the cone,…