Which of the following triangles is similar to the ΔPQR?
Similar figures have same shape but not necessarily of same size.
ΔPQR is a right triangle. [From the figure.]
ΔPNS, ΔSRN, and ΔSQM are not similar to ΔPQR as they are not right triangles.
From the given choices the triangle that is similar to ΔPQR is ΔQRS.
Correct answer : (1)
What is the surface area of the cylinder shown?
Correct answer : (4)
The diameter of a roller is 110 cm and its length is 150 cm. It takes 800 complete revolutions to move once over a play ground to level it. Find the area of the play ground. [Take = 3.]
Area of the play ground = No. of revolutions × Curved surface area of the rollers. [Formula.]
Radius of the roller = = 55 cm Length of the roller = 150cm [Radius = .]
Curved surface area = 2 × 3 × 55 × 150 = 49500 cm2 [Curved surface area = 2 .]
Area of the play ground = = 3960 m2 [Substitute in step1 and simplify.] [1m = 100cm.]
Correct answer : (3)
The inner diameter of a circular well is 7 m and it is 6 m deep. Find the cost of plastering its inner curved surface at the rate of $25 per sq m.[Take = 3.]
Cost of plastering = (Rate of plastering) × (Inner curved surface area). [Formula.]
Inner radius = = 3.50 m [Radius = .]
Depth = 6 m [Given.]
Inner surface area = 3 × 3.50 × 6 = 63 m2 [Well is in the form of a cylinder.] [Inner surface area of a cylinder = .]
Rate of plastering per sq.m = $25 [Given.]
Cost of plastering = 25 × 63 = $1575 [Substitute in step1 and simplify.]
Correct answer : (2)
A closed circular water tank of outer diameter 4 m and height 2 m is to be painted. Find the total charges for painting if the rate of painting is $10 per sq.m.[Take = 3.]
Cost of painting = (Rate of painting) × (total surface area of the tank). [Formula.]
Total surface area = Curved surface area + area of the end faces. [Analysis.]
Radius = = 2 m
Height = 2 m. [Given.]
Curved surface area = 2 × 3 × 2 × 2 = 24 sq.m [Curved surface area = 2 .]
Area of the end faces = 2 × 3 × 22 = 24 sq.m [Area of end faces = 2 2.]
Total surface area = 24 + 24 = 48 sq.m [Substitute in step2.]
Rate of painting = $10 per sq.m
Cost of painting = 10 × 48 = $480 [Substitute in step1 and simplify.]
Correct answer : (4)
A cylindrical open vessel is to be made of a thin sheet of uniform thickness. If the diameter of the vessel is 30 cm and the height is 22 cm, then find the area of the sheet required to make it. [Take = 3.]
Area of the sheet = Curved surface area of the cylinder + Base area of the vessel. [Analysis.]