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 height of the cylinder is 10 cm and its base is of radius 3.5 cm, find the total surface area of the article. Ans: The curved surface area of the […]
surface areas and volumes
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 hallowed out. Find the total surface area of the remaining solid. Ans: Let’s draw the diagram to capture the shape: Total surface area of the cylinder: = curved surface area of
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 have adequate space for parking. After survey, it was decided to build rectangular playground, with a semi-circular area allotted for parking at one end of the playground. The length and
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. The diameter of the model is 3 cm and its total length is 12 cm. If each cone has a height of 2 cm, find the volume of air contained
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 a circle as shown in the figure. Find the area of the shaded region. (Use = 3.14) Ans: VIDEO SOLUTION STEP BY STEP SOLUTION Since the rectangle is inscribed inside
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 cm and the other is hemispherical with diameter 21 cm. Based on the above, answer the following questions: (i) Find the area of the base of the cylindrical cup. (ii)
Q) Can any rational value of x make the new area equal to 220 cm2 ? [ Click here for full question] Ans: If by increasing each dimension by x units, the area of the photo is enlarged to 220 cm2, then (18 + x) (12 + x) = 220 ⇒ x2 + 30 x
Can any rational value of x make the new area equal to 220cm2 Read More »
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 units each to double the area of the photo. The original photo is 18 cm long and 12 cm wide. Based on the above information, answer the following questions: (i)
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 part. Fine the total height of the room if it Contains m3 of air. Take Ans: Let h be the height of cylindrical part and r be the radius of
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, which is th of volume of the cone, is unfilled but hemisphere is formed on the top. Find volume of the of ice-cream. Ans: VIDEO SOLUTION STEP BY STEP SOLUTION