Math practice questions are given in the worksheet on prism. The questions are mainly based on word problems on prism and problems based on finding volume and surface area of triangular prism, rectangular prism and right prism.

**1.** The base of a right prism is an equilateral triangle of side a cm. If h cm. be the-height of the prism show that the area of its lateral surface is 3ah square cm. and volume is (√3/4) a²h cubic cm. **2.** The base of a right prism is a triangle whose sides are of lengths 9 cm. 10 cm. and 11 cm. Find the volume and total surface area of the prism if its height be 15 cm. **3.** Find the volume and lateral surface of a right prism 8 inches high standing on an isosceles triangle, each of whose equal sides is 5 inches and the other side 6 inches.

**4.** The cross-section of a right prism is an equilateral triangle of side 4 centimeters. If the volume of the prism be 60√3 cubic centimeters, find its height. Find also the total surface area of the prism. **5.** The volume of a right prism is 80 cu. ft and its base is a triangle whose sides are 3 ft., 4 ft. and 5 ft. Find the height and the total surface of the prism.

**6.** The base of a right prism is a trapezium whose parallel sides are 8 m. and 12m. in length and the distance between them is 7 m. If the volume of the prism 840 m³, find its height.**7.** The base of a right prism is a trapezium whose parallel sides are 8 ft. and 11ft. in length. If the height of the prism is 11 ft and volume 1100 cubic feet, then find the perpendicular distance between the parallel sides of the trapezium.**8.** The base of a right prism is a trapezoid whose parallel sides are of lengths 15 cm. and 23 cm. and one of the remaining sides is of length 15 cm. and perpendicular to the parallel sides. If the volume of the prism be 5700 c.c., find its height and the area of its whole surface.**9.** The base of a right prism is a triangle whose perimeter is 15 cm. and length of the in-radius of the triangle is 3 cm. If the volume of the prim be 270 c.c., find its height.**10.** If the cross-section of a right prism is a regular hexagon of side 12 metres and its height is 20 metres, find the area of the total lateral surface and the volume of the prism.**11.** The height of a right prism is 6√3 cm. and its base is a regular hexagon of side 5 cm. Find the volume and the area of the lateral surface of the prism.**12.** A right prism stands on a base which is a regular hexagon of side 15 cm. If the area of its lateral surface be 5400 sq. cm., find its height. Find also the volume of the prism.**13.** The base of a right prism is a regular hexagon whose side is 6 ft. If the area of its total surface be 288√3 sq. ft., find its volume.**14.** The base of a right prism is a regular hexagon and its side-edges is 15 cm. If the volume of the prism be 144O√3 c.c., find the area of its whole surface.**15.** The area of whole surface of a right prism is 1008 sq. cm. and its base is a triangle whose sides are 18 cm., 20 cm. and 34 cm. Find the height and volume of the prism.**16.** The height of a right prism is 15 m. and its base is a square. If the area of its whole surface be 608 sq. m., find its volume.**17.** The area of the lateral surface of a right prism is 378 sq. m. and its height is 12 m. If the base is a regular nonagon, find the length of each side of the base.**18.** Two prisms of equal height are such that the magnitude of base of one is double the perimeter of the base of the other. Prove that the magnitude of the volume of the first prism is double the area of the lateral surface of the other prism.**19.** The height of a right prism is 15 cm. and its base is a regular octagon whose each side is 10 cm. Show that the volume of the prism is nearly 7242 c.c.**20.** The whole surface of a right prism 15 cm. high is 675√3 sq. cm. if the base is a regular hexagon, then find the length of each side of the base and the volume of the prism.**21.** The base of a right prism is a regular pentagon of side x. If the area of its lateral surface and volume be s and v respectively, show that:

x = (4v/s) tan 36°

**22.** The base of a right prism is a regular octagon. If its height, lateral surface and volume be h, S and v respectively, prove that,

S² = 32 vh tan (π/8).

**23.** The height of a right prism is 15 cm. and its volume is 750(√2 - 1) C.C. If the base be a regular octagon, find the length of each side of the base.

**24.** Through an iron pipe whose water flows uniformly at the rate of 25 cm. per second. How long will it take to discharge 90 litre?

**25.** A vertical column, 10 m. high has a rectangular cross-section of length 45 cm. and breadth 35 cm. Find the cost of painting its vertical surfaces at the rate of $ 240 per square metre.

**26.** The height of a metallic right prism is 20 cm. and its base is a trapezium whose parallel sides are of lengths 6 cm. and 3 cm. and the perpendicular distance between them is 10 cm. If one cubic centimetre of the metal weighs 6 gm. and the price of one kilogram of metal be $ 20, find the cost of the prism.

Answers for the worksheet on prism are given below to check the exact answers of the above questions on volume and surface area of a prism.

**2.** 450√2c.c. and (450 + 60√2) sq. cm.;

**3.** 96 cu. inches and 128 sq. inches;

**4.** l5 cm. and 4(45 + 2√3) sq. cm.;

**5.** 40/3ft and 172 sq. ft.

**6.** 12 m.

**7.** 10 ft;

**8.** 20 cm. and 1970 sq. cm.

**9.** 12 cm.

**10.** 1440 sq.m. and 4320 √3 cu.m

**11.** 675 c.c. and 180√3 sq. cm

**12.** 60 cm. and 20250√3 c.c.

**13.** 810 cu. ft.

**14.** (720 + 192√3) sq. cm.

**15.** 10 cm. and 1440 c.c.

**16.** 960 cu. m

**17.** 3.5 m.

**20.** 5√3 cm. and (3375√3)/2 c.c

**23.** 5 (√2- 1) cm.

**24.** 25 sec.

**25.** $ 38.40

**26.** $ 108.

**●**** Mensuration**

**Formulas for 3D Shapes****Volume and Surface Area of the Prism****Worksheet on Volume and Surface Area of Prism****Volume and Whole Surface Area of Right Pyramid****Volume and Whole Surface Area of Tetrahedron****Volume of a Pyramid****Volume and Surface Area of a Pyramid****Problems on Pyramid****Worksheet on Volume and Surface Area of a Pyramid****Worksheet on Volume of a Pyramid**

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